Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights

TL;DR

This paper investigates higher order Kirchhoff type Choquard equations with exponential non-linearity and singular weights, establishing existence results using variational methods and inequalities.

Contribution

It introduces new existence results for Kirchhoff Choquard problems with exponential non-linearity and singular weights, employing Mountain pass and Nehari manifold techniques.

Findings

Existence of solutions via Mountain pass Lemma.

Multiple solutions using Nehari manifold approach.

Application of Moser-Trudinger and Adams-Moser inequalities.

Abstract

In this work, we study the higher order Kirchhoff type Choquard equation $(KC)$ involving a critical exponential non-linearity and singular weights. We prove the existence of solution to $(KC)$ using Mountain pass Lemma in light of Moser-Trudinger and singular Adams-Moser inequalities. In the second part of the paper, using the Nehari manifold technique and minimization over its suitable subsets, we prove the existence of at least two solutions to the Kirchhoff type Choquard equation $(\mathcal{P_{\la,M}})$ involving convex-concave type non-linearity.