High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

Abstract

This article deals with the study of the following Kirchhoff–Choquard problem: (Formula presented.) where M models Kirchhoff-type nonlinear term of the form M(t)=a+btθ-1, where a,b>0 are given constants; 1<p<N, Δp=div(|∇u|p-2∇u) is the p-Laplacian operator; potential V∈C2(RN); f is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for θ∈1,2N-μN-p via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem. © The Author(s) 2024.