Unbounded components of positive radial solutions for semilinear indefinite Neumann problems.
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| Titel: | Unbounded components of positive radial solutions for semilinear indefinite Neumann problems. |
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| Autoren: | Ma, Ruyun1 (AUTHOR), Yang, Wei1 (AUTHOR) wyang_nwnu@163.com, Shi, Xuanrong1 (AUTHOR) |
| Quelle: | Complex Variables & Elliptic Equations. Dec2025, Vol. 70 Issue 12, p2051-2071. 21p. |
| Schlagwörter: | *NEUMANN problem, *BIFURCATION theory, *DIFFERENTIAL equations, *ASYMPTOTIC expansions, *PARTIAL differential equations |
| Abstract: | We are concerned with the semilinear Neumann problem (P) \[ \begin{cases} -\Delta u+b(|x|)x\cdot\nabla u=\lambda h(|x|)f(u), & {\rm in}\ B,\\ \partial_{v}u=0, & {\rm on}\ \partial B, \end{cases} \] { − Δ u + b (| x |) x ⋅ ∇u = λh (| x |) f (u) , in B , ∂ v u = 0 , on ∂B , where $ \lambda >0 $ λ > 0 is a parameter, B is a unit open ball in $ \mathbb {R}^{N}, N\geqslant 2 $ R N , N ⩾ 2 , $ b\in C([0,1],(-\infty,0]) $ b ∈ C ([ 0 , 1 ] , (− ∞ , 0 ]) , $ h\in C([0,1],\mathbb {R}) $ h ∈ C ([ 0 , 1 ] , R) and $ f\in C([0,\infty),[0,\infty)) $ f ∈ C ([ 0 , ∞) , [ 0 , ∞)) satisfies sublinear growth at infinity and asymptotic linear growth at zero. Under some suitable conditions, we show the existence of S-shaped component of positive radial solutions for Neumann problem (P). The proof of our main result is based upon bifurcation techniques. [ABSTRACT FROM AUTHOR] |
| Datenbank: | Academic Search Index |
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Nájsť tento článok vo Web of Science | Abstract: | We are concerned with the semilinear Neumann problem (P) \[ \begin{cases} -\Delta u+b(|x|)x\cdot\nabla u=\lambda h(|x|)f(u), & {\rm in}\ B,\\ \partial_{v}u=0, & {\rm on}\ \partial B, \end{cases} \] { − Δ u + b (| x |) x ⋅ ∇u = λh (| x |) f (u) , in B , ∂ v u = 0 , on ∂B , where $ \lambda >0 $ λ > 0 is a parameter, B is a unit open ball in $ \mathbb {R}^{N}, N\geqslant 2 $ R N , N ⩾ 2 , $ b\in C([0,1],(-\infty,0]) $ b ∈ C ([ 0 , 1 ] , (− ∞ , 0 ]) , $ h\in C([0,1],\mathbb {R}) $ h ∈ C ([ 0 , 1 ] , R) and $ f\in C([0,\infty),[0,\infty)) $ f ∈ C ([ 0 , ∞) , [ 0 , ∞)) satisfies sublinear growth at infinity and asymptotic linear growth at zero. Under some suitable conditions, we show the existence of S-shaped component of positive radial solutions for Neumann problem (P). The proof of our main result is based upon bifurcation techniques. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 17476933 |
| DOI: | 10.1080/17476933.2024.2448666 |