Abstract
In this article, we study the Brezis-Nirenberg result for Kirchhoff-type equation in dimension four. Using the variational method, the existence of positive solutions and the multiplicity of solutions are obtained. It is worth to point out that a global Palais-Smale compactness condition for the critical problem is obtained. Thanks to this global Palais-Smale compactness condition, k pairs of distinct solutions are obtained, where .
Disclosure statement
No potential conflict of interest was reported by the authors.