Asymptotic behavior of the variational eigenvalues for semilinear sturm-liouville problems

DOI10.1016/0362-546X(92)90130-7zbMath0768.34057OpenAlexW2070473543MaRDI QIDQ4030862

Tetsutaro Shibata

Publication date: 1 April 1993

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(92)90130-7

zbMATH Keywords

asymptotic behaviourvariational eigenvaluesLjusternik- Schnirelman theorysemi-linear Sturm-Liouville problem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (7)

Asymptotic formulas of eigenvalues and eigenfunctions of non-autonomous semilinear Sturm-Liouville problems ⋮ Variational method for precise asymptotic formulas for nonlinear eigenvalue problems ⋮ Asymptotic behavior of eigenvalues for two-parameter perturbed elliptic sine-Gordon type equations ⋮ Two-parameter nonlinear Sturm-Liouville problems ⋮ Spectral asymptotics of two parameter nonlinear Sturm-Liouville problem ⋮ Precise spectral asymptotics for the Dirichlet problem \(-u(t)+g(u(t))=\lambda\sin u(t)\) ⋮ Precise spectral asymptotics for nonlinear Sturm-Liouville problems

Cites Work

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• Nodal properties and variational characterizations of solutions to nonlinear Sturm-Liouville problems
• Le nombre de solutions de certains problèmes semi-linéaires elliptiques

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