Ground state solution to n-kirchhoff equation with critical exponential growth and without ambrosetti–rabinowitz condition

Abstract

This article is focused on the existence of a ground state solution to the Kirchhoff problem:

where is a bounded domain with smooth boundary and . We assume that f satisfies critical exponential growth at infinity but does not satisfy the well-known Ambrosetti–Rabinowitz condition. We prove the existence of a ground state weak solution via mountain pass theorem and Nehari manifold technique.