Spectral properties of some regular boundary value problems for fourth order differential operators

In this paper we consider the problem where λ is a spectral parameter; p j ( x ) ∈ L 1 (0, 1), j = 0, 1, 2, are complex-valued functions; α s;l , s = 1, 2, 3, , are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic fo...

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Podrobná bibliografie
Vydáno v:	Central European journal of mathematics Ročník 11; číslo 1; s. 94 - 111
Hlavní autoři:	Kerimov, Nazim B., Kaya, Ufuk
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Heidelberg SP Versita 01.01.2013 Versita De Gruyter Brill Sp. z o.o., Paradigm Publishing Services De Gruyter
Témata:	34B05 34L10 34L20 Algebra Asymptotic behavior of eigenvalues and eigenfunctions Basis properties of the system of root functions Boundary conditions Boundary value problems Complex constants Differential equations Eigenvalues Eigenvectors Fourth order eigenvalue problem Geometry Lie Groups Mathematics Mathematics and Statistics Not strongly regular boundary conditions Number Theory Operators (mathematics) Probability Theory and Stochastic Processes Research Article Spectra Topological Groups Asymptotic behavior of eigenvalues and eigenfunctions 34B05 Fourth order eigenvalue problem Basis properties of the system of root functions Not strongly regular boundary conditions 34L10 34L20
ISSN:	1895-1074, 1644-3616, 2391-5455
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Popis
Shrnutí:	In this paper we consider the problem where λ is a spectral parameter; p j ( x ) ∈ L 1 (0, 1), j = 0, 1, 2, are complex-valued functions; α s;l , s = 1, 2, 3, , are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established in the case α 3,2 + α 1,0 ≠ α 2,1 . It is proved that the system of root functions of this spectral problem forms a basis in the space L p (0, 1), 1 < p < ∞, when α 3,2 + α 1,0 ≠ α 2,1 , p j ( x ) ∈ W 1 j (0, 1), j = 1, 2, and p 0 ( x ) ∈ L 1 (0, 1); moreover, this basis is unconditional for p = 2.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1895-1074 1644-3616 2391-5455
DOI:	10.2478/s11533-012-0059-x