The Rabinowitz-Floer homology for a class of semilinear problems and applications

TL;DR

This paper develops a Rabinowitz-Floer homology framework for certain nonlinear problems with starshaped potentials, enabling the derivation of existence and multiplicity results for solutions, including equivariant cases.

Contribution

It introduces an explicit Rabinowitz-Floer homology construction for starshaped potentials and applies it to prove solution existence and multiplicity.

Findings

Homology explicitly computed for specific nonlinear problems

Existence of solutions established for several model equations

Multiple solutions identified using the homology framework

Abstract

In this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a \emph{starshaped} potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model equations.