Existence and multiplicity results for Kirchhoff type problems on a double phase setting

TL;DR

This paper investigates the existence and multiplicity of solutions for Kirchhoff type problems within a double phase framework using variational methods in Musielak-Orlicz-Sobolev spaces.

Contribution

It introduces new existence and multiplicity results for Kirchhoff problems on double phase spaces, expanding the understanding of such nonlinear PDEs.

Findings

Existence of solutions established via variational methods.

Multiple solutions demonstrated under certain conditions.

Framework extends classical results to double phase Musielak-Orlicz spaces.

Abstract

In this paper, we study two classes of Kirchhoff type problems set on a double phase framework. That is, the functional space where finding solutions coincides with the Musielak-Orlicz-Sobolev space $W^{1,\mathcal H}_0(\Omega)$, with modular function $\mathcal H$ related to the so called double phase operator. Via a variational approach, we provide existence and multiplicity results.