Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential

TL;DR

This paper investigates the existence and multiplicity of solutions for a class of Kirchhoff-Choquard equations with sign-changing potentials and exponential critical growth nonlinearities in -dimensional space.

Contribution

It establishes new existence and multiplicity results for Kirchhoff-Choquard equations with generalized sign-changing potentials and critical exponential nonlinearities.

Findings

Proved existence of solutions in nondegenerate cases.

Established multiplicity of solutions under certain conditions.

Guaranteed existence of solutions in degenerate cases.

Abstract

In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})\Delta u +Q(x)u + \mu(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ \mu >0 $, $ V $ a sign-changing and possible unbounded potential, $ Q $ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case.