Existence of solutions to four-dimensional Kirchhoff problems with critical-concave nonlinearities

Abstract

We deal with a Kirchhoff problem on a smooth bounded domain of ${\mathbb{R}}^4$ with competing critical and concave terms. By using new approximation techniques and the Nehari manifold analysis, we derive several existence results, complementing earlier ones obtained in the critical-convex case. Compared to similar results in the literature, we provide explicit bounds of the range of the parameters leading to the existence of solutions.