Existence results for double-phase problems via Morse theory

TL;DR

This paper uses Morse theory and cohomological local splitting to establish the existence of nontrivial solutions for double-phase problems, even without a direct sum decomposition.

Contribution

It introduces a novel approach employing Morse theory and cohomological local splitting to analyze double-phase problems without relying on direct sum decomposition.

Findings

Established existence of nontrivial solutions for double-phase problems.

Developed a new method using Morse theory and cohomological local splitting.

Provided estimates of critical groups at zero.

Abstract

We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.