Prescribed energy saddle-point solutions of nonlinear indefinite problems

A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The method is based on application of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which critical points correspond to the solutions of the equation with prescri...

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Bibliographic Details
Published in:Electronic journal of differential equations 2023-03, Vol.2023 (1-37), p.23
Main Authors: Il'yasov, Yavdat, Da Silva, Edcarlos Domingos, Da Silva, Maxwell Lizete
Format: Article
Language:English
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Summary:A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The method is based on application of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which critical points correspond to the solutions of the equation with prescribed energy. An application of the method to nonlinear indefinite elliptic problems with nonlinearities that does not satisfy the Ambrosetti-Rabinowitz growth conditions is also presented.
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2023.23