On a Perturbed Critical p-Kirchhoff-Type Problem

Abstract

In this paper we deal with a stationary non-degenerate $p-$Kirchhoff type problem with critical non-linearity and a subcritical parametrized perturbation. We work on bounded domains of the Euclidean space, without any restriction on the dimension or on $p>0$. Variational methods will be utilized in combination with an analysis of the fibering functions of the energy functional, in order to obtain ground state solutions, as well as Mountain Pass solutions, depending on the values of the parameter. A local analysis of the energy functional will allow us to obtain non-trivial solutions even beyond the extremal parameter.