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On the Eigenvalue Accumulation of Sturm‐Liouville Problems Depending Nonlinearly on the Spectral Parameter
Author(s) -
Mennicken R.,
Schmi H.,
Shkalikov A. A.
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981890110
Subject(s) - sturm–liouville theory , eigenvalues and eigenvectors , mathematics , interval (graph theory) , boundary value problem , mathematical analysis , nonlinear system , magnetohydrodynamics , combinatorics , physics , plasma , quantum mechanics
A nonlinear spectral problem for a Sturm‐Liouville equation‐( p (x, λ)y'(x, λ))' + q ( x , λ) y ( x , λ) = 0 on a finite interval [ a , b ] with λ‐dependent boundary conditions is considered. The spectral parameter λ is varying in an interval ∧ and p ( x , λ), q ( x , A) are real, continuous functions on [ a , b ] × ∧ Some criteria to the eigenvalue accumulation at the endpoints of A will be established. The results are applied to concrete problems arising in magnetohydrodynamics.