n-Kirchhoff Choquard equations with exponenetial nonlinearity

TL;DR

This paper investigates the existence and multiplicity of solutions for a Kirchhoff Choquard equation with exponential nonlinearity, employing variational methods and the Moser-Trudinger inequality.

Contribution

It introduces a novel approach using fibering maps and Nehari manifold analysis to establish solution existence and multiplicity for this class of nonlinear equations.

Findings

Existence of weak solutions established.

Multiple solutions demonstrated under certain conditions.

Application of variational methods to exponential nonlinearities.

Abstract

This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see $(KC)$ below). We use the variational method in the light of Moser-Trudinger inequality to show the existence of weak solutions to $(KC)$. Moreover, analyzing the fibering maps and minimizing the energy functional over suitable subsets of the Nehari manifold, we prove existence and multiplicity of weak solutions to convex-concave problem $(\mathcal{P}_{\la,M})$ below.