An application of variational method to nonlinear eigenvalue problem for a class of wave equation

DOI10.1016/0362-546X(82)90055-4zbMath0468.58006OpenAlexW2025298395MaRDI QIDQ3921861

Shaoping Wu

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0362-546x(82)90055-4

zbMATH Keywords

minimaxPalais-Smale conditionvariational duality argumentcritical points of a functional on a manifold in a Banach spaceindex for 1-sphere actionnonlinear eigenvalue problem for wave equation

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Wave equation (35L05) Compact Lie groups of differentiable transformations (57S15) Hamilton-Jacobi theories (49L99)

Cites Work

• Sull'esistenza di autovalori per un problema al contorno non lineare
• Ljusternik-Schnirelman theory and non-linear eigenvalue problems
• A geometrical index for the groupS1 and some applications to the study of periodic solutions of ordinary differential equations
• Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
• Nonlinear Eigenvalue Problems and Group Invariance
• Unnamed Item

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