On the existence of multiple ordered solutions of nonlinear eigenvalue problems

DOI10.1016/0362-546X(87)90066-6zbMath0661.35070OpenAlexW2040343060MaRDI QIDQ3810254

Djairo Guedes de Figueiredo

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0362-546x(87)90066-6

zbMATH Keywords

variational methodsmultiple solutionslocal minimizationbounded domainmountain pass lemmageometrical conditionssemilinearzero boundary dataordered solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (22)

Existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains ⋮ Positive solutions of elliptic problems with locally oscillating nonlinearities ⋮ Unnamed Item ⋮ Critical point theorems and applications to a semilinear elliptic problem ⋮ Multiplicity results and qualitative properties for Neumann semilinear elliptic problems ⋮ Multiple ordered solutions for a class of elliptic problems involving fast increasing weights and nonlinearity with zeros ⋮ Multiple ordered solutions for a class of quasilinear problem with oscillating nonlinearity ⋮ A concave-convex problem with a variable operator ⋮ Multiple positive solutions for a class of variational systems ⋮ Existence and multiplicity of radial positive solutions for a quasilinear elliptic equation with sign-changing nonlinearity ⋮ Semilinear elliptic singular perturbation problems with nonuniform interior behavior ⋮ \(H^1 \cap L^p\) versus \(C^1\) local minimizers ⋮ Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential^∗ ⋮ On positive solutions to equations involving the one-dimensional \(p\)-Laplacian ⋮ Existence and asymptotic behavior of solutions for a class of Neumann problems ⋮ Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann condition ⋮ Boundary layer solutions to functional elliptic equations ⋮ Unnamed Item ⋮ Stable stationary solutions induced by spatial inhomogeneity via ?-convergence ⋮ On the role of diffusivity in some stable equilibria of a diffusion equation ⋮ Families of 'first eigenfunctions' for semilinear elliptic eigenvalue problems ⋮ On positive solutions of elliptic equations with oscillating nonlinearity in \(\mathbb{R}^N\)

Cites Work

• Symmetry and related properties via the maximum principle
• Positive solutions of asymptotically linear elliptic eigenvalue problems
• Variational and topological methods in partially ordered Hilbert spaces
• Dual variational methods in critical point theory and applications
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• On the Existence of Positive Solutions for a Class of Semilinear Elliptic Boundary Value Problems
• A Priori Bounds for Positive Solutions of a Semilinear Elliptic Equation
• On multiple positive solutions of nonlinear elliptic eigenvalue problems

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