A mass supercritical problem revisited
In any dimension N ≥ 1 and for given mass m > 0 , we revisit the nonlinear scalar field equation with an L 2 constraint: - Δ u = f ( u ) - μ u in R N , ‖ u ‖ L 2 ( R N ) 2 = m , u ∈ H 1 ( R N ) , ( P m ) where μ ∈ R will arise as a Lagrange multiplier. Assuming only that the nonlinearity f is con...
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| Vydané v: | Calculus of variations and partial differential equations Ročník 59; číslo 5 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2020
Springer Nature B.V Springer Verlag |
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| ISSN: | 0944-2669, 1432-0835 |
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| Abstract | In any dimension
N
≥
1
and for given mass
m
>
0
, we revisit the nonlinear scalar field equation with an
L
2
constraint:
-
Δ
u
=
f
(
u
)
-
μ
u
in
R
N
,
‖
u
‖
L
2
(
R
N
)
2
=
m
,
u
∈
H
1
(
R
N
)
,
(
P
m
)
where
μ
∈
R
will arise as a Lagrange multiplier. Assuming only that the nonlinearity
f
is continuous and satisfies weak mass supercritical conditions, we show the existence of ground states to
(
P
m
)
and reveal the basic behavior of the ground state energy
E
m
as
m
>
0
varies. In particular, to overcome the compactness issue when looking for ground states, we develop robust arguments which we believe will allow treating other
L
2
constrained problems in general mass supercritical settings. Under the same assumptions, we also obtain infinitely many radial solutions for any
N
≥
2
and establish the existence and multiplicity of nonradial sign-changing solutions when
N
≥
4
. Finally we propose two open problems. |
|---|---|
| AbstractList | In any dimension N ≥ 1 and for given mass m > 0, we revisit the nonlinear scalar field equation with an L 2 constraint: −∆u = f (u) − µu in R N , u 2 L 2 (R N) = m, u ∈ H 1 (R N), (Pm) where µ ∈ R will arise as a Lagrange multiplier. Assuming only that the nonlinearity f is continuous and satisfies weak mass supercritical conditions, we show the existence of ground states to (Pm) and reveal the basic behavior of the ground state energy Em as m > 0 varies. In particular, to overcome the compactness issue when looking for ground states, we develop robust arguments which we believe will allow treating other L 2 constrained problems in general mass supercritical settings. Under the same assumptions, we also obtain infinitely many radial solutions for any N ≥ 2 and establish the existence and multiplicity of nonradial signchanging solutions when N ≥ 4. Finally we propose two open problems. In any dimension N ≥ 1 and for given mass m > 0 , we revisit the nonlinear scalar field equation with an L 2 constraint: - Δ u = f ( u ) - μ u in R N , ‖ u ‖ L 2 ( R N ) 2 = m , u ∈ H 1 ( R N ) , ( P m ) where μ ∈ R will arise as a Lagrange multiplier. Assuming only that the nonlinearity f is continuous and satisfies weak mass supercritical conditions, we show the existence of ground states to ( P m ) and reveal the basic behavior of the ground state energy E m as m > 0 varies. In particular, to overcome the compactness issue when looking for ground states, we develop robust arguments which we believe will allow treating other L 2 constrained problems in general mass supercritical settings. Under the same assumptions, we also obtain infinitely many radial solutions for any N ≥ 2 and establish the existence and multiplicity of nonradial sign-changing solutions when N ≥ 4 . Finally we propose two open problems. In any dimension N≥1 and for given mass m>0, we revisit the nonlinear scalar field equation with an L2 constraint: -Δu=f(u)-μuinRN,‖u‖L2(RN)2=m,u∈H1(RN),(Pm)where μ∈R will arise as a Lagrange multiplier. Assuming only that the nonlinearity f is continuous and satisfies weak mass supercritical conditions, we show the existence of ground states to (Pm) and reveal the basic behavior of the ground state energy Em as m>0 varies. In particular, to overcome the compactness issue when looking for ground states, we develop robust arguments which we believe will allow treating other L2 constrained problems in general mass supercritical settings. Under the same assumptions, we also obtain infinitely many radial solutions for any N≥2 and establish the existence and multiplicity of nonradial sign-changing solutions when N≥4. Finally we propose two open problems. |
| ArticleNumber | 174 |
| Author | Lu, Sheng-Sen Jeanjean, Louis |
| Author_xml | – sequence: 1 givenname: Louis surname: Jeanjean fullname: Jeanjean, Louis email: louis.jeanjean@univ-fcomte.fr organization: Laboratoire de Mathématiques (CNRS UMR 6623), Université de Bourgogne Franche-Comté – sequence: 2 givenname: Sheng-Sen surname: Lu fullname: Lu, Sheng-Sen organization: Center for Applied Mathematics, Tianjin University, School of Mathematical Sciences and LMAM, Peking University |
| BackLink | https://hal.science/hal-03336029$$DView record in HAL |
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| Cites_doi | 10.1137/19M1243907 10.1007/s00220-017-2866-1 10.1007/s00208-020-02000-w 10.1007/BF01626517 10.2140/apde.2019.12.1177 10.1090/tran/7769 10.1016/j.jfa.2020.108610 10.1007/978-1-4612-4146-1 10.1016/j.na.2004.03.034 10.1088/1361-6544/aaf2e0 10.1016/0022-1236(73)90051-7 10.1016/S0362-546X(96)00021-1 10.1007/BF00250556 10.1017/CBO9780511551703 10.1017/S0308210500013147 10.1016/j.jfa.2009.09.013 10.1112/plms/pds072 10.1007/BF01941322 10.1515/ans-2014-0104 10.1016/0022-1236(82)90072-6 10.1016/j.jfa.2017.01.025 10.2307/2044999 10.1016/j.anihpc.2006.01.003 10.1016/j.jfa.2018.02.007 10.1007/s00208-018-1666-z 10.1016/j.matpur.2016.03.004 10.1515/ans-2004-0411 10.1088/1361-6544/ab435e 10.1007/s00013-012-0468-x 10.1007/BF00250555 10.1016/j.na.2019.111604 10.4171/JEMS/351 10.1006/jfan.1993.1133 10.1016/j.jde.2020.05.016 10.1016/S0294-1449(16)30428-0 10.1090/cbms/065 10.1016/S0294-1449(16)30422-X 10.1515/ans-2008-0302 10.1007/s00526-018-1476-x 10.1016/j.jfa.2021.108989 |
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| Copyright | Springer-Verlag GmbH Germany, part of Springer Nature 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020. Distributed under a Creative Commons Attribution 4.0 International License |
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| Issue | 5 |
| Keywords | 35Q55 35J60 Mass supercritical cases Radial and nonradial solutions Sign-changing solutions Ground states 35Q55 Nonlinear scalar field equations |
| Language | English |
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| PublicationTitle | Calculus of variations and partial differential equations |
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| References | Bartsch, Zhang, Zou (CR9) 2020 Lions (CR30) 1982; 49 Ghoussoub (CR21) 1993 Lorca, Ubilla (CR34) 2004; 58 Musso, Pacard, Wei (CR36) 2012; 14 Berestycki, Cazenave (CR13) 1981; 293 Palais (CR38) 1979; 69 Jeanjean, Lu (CR26) 2020; 190 CR19 CR39 CR16 Liu, Wang (CR33) 2004; 4 CR35 Cingolani, Jeanjean (CR20) 2019; 51 CR32 Berestycki, Lions (CR14) 1983; 82 CR31 Bartsch, Soave (CR5) 2017; 272 Bartsch, Willem (CR8) 1993; 117 Szulkin, Weth (CR43) 2009; 257 Jeanjean (CR25) 1999; 129 Bonheure, Casteras, Gou, Jeanjean (CR17) 2019; 372 Le Coz (CR28) 2008; 8 Ikoma (CR22) 2014; 14 Ambrosetti, Rabinowitz (CR2) 1973; 14 Strauss (CR42) 1977; 55 Brezis, Lieb (CR18) 1983; 88 Bellazzini, Georgiev, Visciglia (CR11) 2018; 371 Willem (CR45) 1996 Soave (CR40) 2020; 269 Ackermans, Weth (CR1) 2019; 12 Szulkin, Weth (CR44) 2010 CR7 Bartsch, Jeanjean, Soave (CR4) 2016; 106 Bartsch, Soave (CR6) 2018; 275 Noris, Tavares, Verzini (CR37) 2019; 32 Jeanjean, Lu (CR27) 2019; 32 Bartsch, De Valeriola (CR3) 2013; 100 Berestycki, Lions (CR15) 1983; 82 Li, Wang, Zeng (CR29) 2006; 23 Soave (CR41) 2020; 279 Bellazzini, Jeanjean, Luo (CR12) 2013; 107 Bellazzini, Boussaid, Jeanjean, Visciglia (CR10) 2017; 353 Ikoma, Tanaka (CR23) 2019; 24 Jeanjean (CR24) 1997; 28 L Jeanjean (1828_CR26) 2020; 190 J Bellazzini (1828_CR10) 2017; 353 A Ambrosetti (1828_CR2) 1973; 14 Y Li (1828_CR29) 2006; 23 L Jeanjean (1828_CR27) 2019; 32 N Ikoma (1828_CR23) 2019; 24 1828_CR19 S Lorca (1828_CR34) 2004; 58 1828_CR16 N Ikoma (1828_CR22) 2014; 14 T Bartsch (1828_CR8) 1993; 117 S Cingolani (1828_CR20) 2019; 51 P-L Lions (1828_CR30) 1982; 49 1828_CR39 1828_CR7 T Bartsch (1828_CR9) 2020 1828_CR32 J Bellazzini (1828_CR12) 2013; 107 1828_CR35 M Willem (1828_CR45) 1996 S Le Coz (1828_CR28) 2008; 8 1828_CR31 H Berestycki (1828_CR14) 1983; 82 N Soave (1828_CR40) 2020; 269 T Bartsch (1828_CR4) 2016; 106 T Bartsch (1828_CR6) 2018; 275 N Soave (1828_CR41) 2020; 279 M Musso (1828_CR36) 2012; 14 H Berestycki (1828_CR13) 1981; 293 L Jeanjean (1828_CR25) 1999; 129 N Ackermans (1828_CR1) 2019; 12 T Bartsch (1828_CR3) 2013; 100 Z Liu (1828_CR33) 2004; 4 A Szulkin (1828_CR44) 2010 J Bellazzini (1828_CR11) 2018; 371 RS Palais (1828_CR38) 1979; 69 N Ghoussoub (1828_CR21) 1993 L Jeanjean (1828_CR24) 1997; 28 D Bonheure (1828_CR17) 2019; 372 H Brezis (1828_CR18) 1983; 88 B Noris (1828_CR37) 2019; 32 A Szulkin (1828_CR43) 2009; 257 WA Strauss (1828_CR42) 1977; 55 T Bartsch (1828_CR5) 2017; 272 H Berestycki (1828_CR15) 1983; 82 |
| References_xml | – volume: 51 start-page: 3533 year: 2019 end-page: 3568 ident: CR20 article-title: Stationary waves with prescribed -norm for the planar Schrödinger–Poisson system publication-title: SIAM J. Math. Anal. doi: 10.1137/19M1243907 – volume: 8 start-page: 455 year: 2008 end-page: 463 ident: CR28 article-title: A note on Berestycki–Cazenave classical instability result for nonlinear Schrödinger equations publication-title: Adv. Nonlinear Stud. – volume: 353 start-page: 229 year: 2017 end-page: 251 ident: CR10 article-title: Existence and stability of standing waves for supercritical NLS with a partial confinement publication-title: Comm. Math. Phys. doi: 10.1007/s00220-017-2866-1 – volume: 293 start-page: 489 year: 1981 end-page: 492 ident: CR13 article-title: Instabilités des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaire publication-title: C. R. Acad. Sci. Paris – year: 2020 ident: CR9 article-title: Normalized solutions for a coupled Schrödinger system publication-title: Math. Annalen doi: 10.1007/s00208-020-02000-w – volume: 55 start-page: 149 year: 1977 end-page: 162 ident: CR42 article-title: Existence of solitary waves in higher dimensions publication-title: Comm. Math. Phys. doi: 10.1007/BF01626517 – ident: CR39 – volume: 12 start-page: 1177 year: 2019 end-page: 1213 ident: CR1 article-title: Unstable normalized standing waves for the space periodic NLS publication-title: Anal. PDE doi: 10.2140/apde.2019.12.1177 – ident: CR16 – volume: 372 start-page: 2167 year: 2019 end-page: 2212 ident: CR17 article-title: Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime publication-title: Trans. Am. Math. Soc. doi: 10.1090/tran/7769 – volume: 279 start-page: 108610 year: 2020 ident: CR41 article-title: Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2020.108610 – year: 1996 ident: CR45 publication-title: Minimax Theorems doi: 10.1007/978-1-4612-4146-1 – volume: 58 start-page: 961 year: 2004 end-page: 968 ident: CR34 article-title: Symmetric and nonsymmetric solutions for an elliptic equation on publication-title: Nonlinear Anal. doi: 10.1016/j.na.2004.03.034 – volume: 32 start-page: 1044 year: 2019 end-page: 1072 ident: CR37 article-title: Normalized solutions for nonlinear Schrödinger systems on bounded domains publication-title: Nonlinearity doi: 10.1088/1361-6544/aaf2e0 – volume: 14 start-page: 349 year: 1973 end-page: 381 ident: CR2 article-title: Dual variational methods in critical points theory and applications publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(73)90051-7 – ident: CR35 – volume: 28 start-page: 1633 year: 1997 end-page: 1659 ident: CR24 article-title: Existence of solutions with prescribed norm for semilinear elliptic equations publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(96)00021-1 – volume: 82 start-page: 347 year: 1983 end-page: 375 ident: CR15 article-title: Nonlinear scalar field equations II: existence of infinitely many solutions publication-title: Arch. Rat. Mech. Anal. doi: 10.1007/BF00250556 – year: 1993 ident: CR21 publication-title: Duality and Perturbation Methods in Critical Point Theory doi: 10.1017/CBO9780511551703 – volume: 129 start-page: 787 year: 1999 end-page: 809 ident: CR25 article-title: On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer type problem set on publication-title: Proc. Roy. Soc. Edinb. A doi: 10.1017/S0308210500013147 – volume: 24 start-page: 609 year: 2019 end-page: 646 ident: CR23 article-title: A note on deformation argument for normalized solutions of nonlinear Schrödinger equations and systems publication-title: Adv. Differ. Equ. – volume: 257 start-page: 3802 year: 2009 end-page: 3822 ident: CR43 article-title: Ground state solutions for some indefinite variational problems publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2009.09.013 – volume: 107 start-page: 303 year: 2013 end-page: 339 ident: CR12 article-title: Existence and instability of standing waves with prescribed norm for a class of Schrödinger–Poisson equations publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/pds072 – ident: CR19 – volume: 69 start-page: 19 year: 1979 end-page: 30 ident: CR38 article-title: The principle of symmetric criticality publication-title: Commun. Math. Phys. doi: 10.1007/BF01941322 – start-page: 597 year: 2010 end-page: 632 ident: CR44 publication-title: The Method of Nehari Manifold – volume: 14 start-page: 115 year: 2014 end-page: 136 ident: CR22 article-title: Compactness of minimizing sequences in nonlinear Schrödinger systems under multiconstraint conditions publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2014-0104 – volume: 49 start-page: 315 year: 1982 end-page: 344 ident: CR30 article-title: Symétrie et compacité dans les espaces de Sobolev publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(82)90072-6 – volume: 272 start-page: 4998 year: 2017 end-page: 5037 ident: CR5 article-title: A natural constraint approach to normalized solutions on nonlinear Schrödinger equations and systems publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2017.01.025 – ident: CR31 – volume: 88 start-page: 486 year: 1983 end-page: 490 ident: CR18 article-title: A relation between pointwise convergence of functions and convergence of functionals publication-title: Proc. Am. Math. Soc. doi: 10.2307/2044999 – volume: 23 start-page: 829 year: 2006 end-page: 837 ident: CR29 article-title: Ground states of nonlinear Schrödinger equations with potentials publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire doi: 10.1016/j.anihpc.2006.01.003 – volume: 275 start-page: 516 year: 2018 end-page: 521 ident: CR6 article-title: Correction to “A natural constraint approach to normalized solutions on nonlinear Schrödinger equations and systems” [J. Funct. Anal. 272 (2017) 4998–5037] publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2018.02.007 – volume: 371 start-page: 707 year: 2018 end-page: 740 ident: CR11 article-title: Long time dynamics for semi-relativistic NLS and half wave in arbitrary dimension publication-title: Math. Ann. doi: 10.1007/s00208-018-1666-z – volume: 106 start-page: 583 year: 2016 end-page: 614 ident: CR4 article-title: Normalized solutions for a system of coupled cubic Schrödinger equations on publication-title: J. Math. Pure Appl. doi: 10.1016/j.matpur.2016.03.004 – ident: CR32 – volume: 4 start-page: 561 year: 2004 end-page: 572 ident: CR33 article-title: On the Ambrosetti–Rabinowitz superlinear condition publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2004-0411 – volume: 32 start-page: 4942 year: 2019 end-page: 4966 ident: CR27 article-title: Nonradial normalized solutions for nonlinear scalar field equations publication-title: Nonlinearity doi: 10.1088/1361-6544/ab435e – ident: CR7 – volume: 100 start-page: 75 year: 2013 end-page: 83 ident: CR3 article-title: Normalized solutions of nonlinear Schrödinger equations publication-title: Arch. Math. doi: 10.1007/s00013-012-0468-x – volume: 82 start-page: 313 year: 1983 end-page: 346 ident: CR14 article-title: Nonlinear scalar field equations I: existence of a ground state publication-title: Arch. Rat. Mech. Anal. doi: 10.1007/BF00250555 – volume: 190 start-page: 111604 year: 2020 ident: CR26 article-title: Nonlinear scalar field equations with general nonlinearity publication-title: Nonlinear Anal. doi: 10.1016/j.na.2019.111604 – volume: 14 start-page: 1923 year: 2012 end-page: 1953 ident: CR36 article-title: Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation publication-title: J. Eur. Math. Soc. doi: 10.4171/JEMS/351 – volume: 117 start-page: 447 year: 1993 end-page: 460 ident: CR8 article-title: Infinitely many nonradial solutions of a Euclidean scalar field equation publication-title: J. Funct. Anal. doi: 10.1006/jfan.1993.1133 – volume: 269 start-page: 6941 year: 2020 end-page: 6987 ident: CR40 article-title: Normalized ground states for the NLS equation with combined nonlinearities publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2020.05.016 – volume: 129 start-page: 787 year: 1999 ident: 1828_CR25 publication-title: Proc. Roy. Soc. Edinb. A doi: 10.1017/S0308210500013147 – volume: 14 start-page: 349 year: 1973 ident: 1828_CR2 publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(73)90051-7 – volume: 293 start-page: 489 year: 1981 ident: 1828_CR13 publication-title: C. R. Acad. Sci. Paris – volume: 82 start-page: 347 year: 1983 ident: 1828_CR15 publication-title: Arch. Rat. Mech. Anal. doi: 10.1007/BF00250556 – ident: 1828_CR31 doi: 10.1016/S0294-1449(16)30428-0 – ident: 1828_CR19 – volume: 51 start-page: 3533 year: 2019 ident: 1828_CR20 publication-title: SIAM J. Math. Anal. doi: 10.1137/19M1243907 – ident: 1828_CR39 doi: 10.1090/cbms/065 – volume-title: Minimax Theorems year: 1996 ident: 1828_CR45 doi: 10.1007/978-1-4612-4146-1 – volume: 275 start-page: 516 year: 2018 ident: 1828_CR6 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2018.02.007 – volume: 371 start-page: 707 year: 2018 ident: 1828_CR11 publication-title: Math. Ann. doi: 10.1007/s00208-018-1666-z – volume-title: Duality and Perturbation Methods in Critical Point Theory year: 1993 ident: 1828_CR21 doi: 10.1017/CBO9780511551703 – year: 2020 ident: 1828_CR9 publication-title: Math. Annalen doi: 10.1007/s00208-020-02000-w – volume: 82 start-page: 313 year: 1983 ident: 1828_CR14 publication-title: Arch. Rat. Mech. Anal. doi: 10.1007/BF00250555 – volume: 4 start-page: 561 year: 2004 ident: 1828_CR33 publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2004-0411 – volume: 269 start-page: 6941 year: 2020 ident: 1828_CR40 publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2020.05.016 – volume: 107 start-page: 303 year: 2013 ident: 1828_CR12 publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/pds072 – volume: 69 start-page: 19 year: 1979 ident: 1828_CR38 publication-title: Commun. Math. Phys. doi: 10.1007/BF01941322 – volume: 49 start-page: 315 year: 1982 ident: 1828_CR30 publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(82)90072-6 – start-page: 597 volume-title: The Method of Nehari Manifold year: 2010 ident: 1828_CR44 – volume: 23 start-page: 829 year: 2006 ident: 1828_CR29 publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire doi: 10.1016/j.anihpc.2006.01.003 – ident: 1828_CR32 doi: 10.1016/S0294-1449(16)30422-X – volume: 12 start-page: 1177 year: 2019 ident: 1828_CR1 publication-title: Anal. PDE doi: 10.2140/apde.2019.12.1177 – volume: 117 start-page: 447 year: 1993 ident: 1828_CR8 publication-title: J. Funct. Anal. doi: 10.1006/jfan.1993.1133 – volume: 58 start-page: 961 year: 2004 ident: 1828_CR34 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2004.03.034 – volume: 55 start-page: 149 year: 1977 ident: 1828_CR42 publication-title: Comm. Math. Phys. doi: 10.1007/BF01626517 – volume: 14 start-page: 115 year: 2014 ident: 1828_CR22 publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2014-0104 – volume: 24 start-page: 609 year: 2019 ident: 1828_CR23 publication-title: Adv. Differ. Equ. – volume: 28 start-page: 1633 year: 1997 ident: 1828_CR24 publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(96)00021-1 – volume: 8 start-page: 455 year: 2008 ident: 1828_CR28 publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2008-0302 – volume: 106 start-page: 583 year: 2016 ident: 1828_CR4 publication-title: J. Math. Pure Appl. doi: 10.1016/j.matpur.2016.03.004 – volume: 100 start-page: 75 year: 2013 ident: 1828_CR3 publication-title: Arch. Math. doi: 10.1007/s00013-012-0468-x – ident: 1828_CR7 doi: 10.1007/s00526-018-1476-x – volume: 353 start-page: 229 year: 2017 ident: 1828_CR10 publication-title: Comm. Math. Phys. doi: 10.1007/s00220-017-2866-1 – volume: 257 start-page: 3802 year: 2009 ident: 1828_CR43 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2009.09.013 – ident: 1828_CR35 – volume: 372 start-page: 2167 year: 2019 ident: 1828_CR17 publication-title: Trans. Am. Math. Soc. doi: 10.1090/tran/7769 – volume: 32 start-page: 1044 year: 2019 ident: 1828_CR37 publication-title: Nonlinearity doi: 10.1088/1361-6544/aaf2e0 – volume: 190 start-page: 111604 year: 2020 ident: 1828_CR26 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2019.111604 – volume: 272 start-page: 4998 year: 2017 ident: 1828_CR5 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2017.01.025 – ident: 1828_CR16 doi: 10.1016/j.jfa.2021.108989 – volume: 88 start-page: 486 year: 1983 ident: 1828_CR18 publication-title: Proc. Am. Math. Soc. doi: 10.2307/2044999 – volume: 279 start-page: 108610 year: 2020 ident: 1828_CR41 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2020.108610 – volume: 14 start-page: 1923 year: 2012 ident: 1828_CR36 publication-title: J. Eur. Math. Soc. doi: 10.4171/JEMS/351 – volume: 32 start-page: 4942 year: 2019 ident: 1828_CR27 publication-title: Nonlinearity doi: 10.1088/1361-6544/ab435e |
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| Snippet | In any dimension
N
≥
1
and for given mass
m
>
0
, we revisit the nonlinear scalar field equation with an
L
2
constraint:
-
Δ
u
=
f
(
u
)
-
μ
u
in
R
N
,
‖
u
‖
L... In any dimension N≥1 and for given mass m>0, we revisit the nonlinear scalar field equation with an L2 constraint:... In any dimension N ≥ 1 and for given mass m > 0, we revisit the nonlinear scalar field equation with an L 2 constraint: −∆u = f (u) − µu in R N ,... |
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| SubjectTerms | Analysis Analysis of PDEs Calculus of Variations and Optimal Control; Optimization Constraints Control Ground state Lagrange multiplier Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinearity Scalars Systems Theory Theoretical |
| Title | A mass supercritical problem revisited |
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