An abstract critical point theorem with applications to elliptic problems with combined nonlinearities

2021/02/18 by Kanishka Perera, Perera, Kanishka · 2 citations
Mathematics · #35R11 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Primary 58E05 #Secondary 35J92

paper · pdf · doi:10.48550/arxiv.2102.09131

openalex publication_date 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial higher critical groups. This theorem yields pairs of nontrivial solutions that are neither local minimizers nor of mountain pass type for problems with combined nonlinearities. Applications are given to subcritical and critical p-Laplacian problems, Kirchhoff type nonlocal problems, and critical fractional p-Laplacian problems.

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• On a scaled abstract linking theorem with an application to the Schrödinger--Poisson--Slater equation

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