Multiple Nontrivial Solutions for Superlinear Double Phase Problems Via Morse Theory

Abstract

The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools together with suitable truncation and minimax techniques with Morse theory, the authors prove the existence of one and three nontrivial weak solutions, respectively.

Keywords

Double phase problems / Musielak-Orlicz space / Variational method / Critical groups / Nonlinear regularity / Multiple solution

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