Multiplicity of solutions for nonlinear coercive problems

We are concerned in this paper with problems that involve nonlinear potential mappings satisfying condition (S) and whose potentials are coercive. We first provide mild sufficient conditions for the minimizing sequence in the Weierstrass-Tonelli theorem in order to have strongly convergent subsequences. Next, we establish a three critical point theorem which is based on the Pucci-Serrin type mountain pass lemma and which is an infinite dimensional counterpart of the Courant theorem. Ricceri-type three critical point results then follow. Some applications to Dirichlet boundary value problems driven by the perturbed Laplacian are given in the final part of this paper.

Keywords

Coercive functional, Multiple solutions, Nonlinear equations

Citation

Journal of Mathematical Analysis and Application. 2023, vol. 528, issue 1, p. 1-13.
https://www.sciencedirect.com/science/article/pii/S0022247X23004766

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/