A non-local p-Kirchhoff critical problem without the Ambrosetti-Rabinowitz condition

In this paper, we study the existence of solutions for a non-local quasi-linear partial differential equation with a critical power in the sense of the Sobolev exponent on the right-hand side plus a subcritical perturbation. After analyzing the levels where we can recover the Cerami condition, we establish some existence results without requiring the Ambrosetti-Rabinowitz condition on the subcritical term. This paper investigates the case where the dimension N of the Euclidean space satisfies p s < N < 2 p s , and it can be seen as a continuation of some of the first author's earlier works, in which the case N > 2 p s was analyzed.