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

Giovanni Anello; Luca Vilasi

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

Analysis of PDEs 2026-07-03 v1

Authors: Giovanni Anello , Luca Vilasi

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.

Keywords

Kirchhoff problem critical nonlinearity concave nonlinearity Nehari manifold existence four-dimensional

Cite

@article{arxiv.2607.03142,
  title  = {Existence of solutions to four-dimensional Kirchhoff problems with critical-concave nonlinearities},
  author = {Giovanni Anello and Luca Vilasi},
  journal= {arXiv preprint arXiv:2607.03142},
  year   = {2026}
}