Multiple solutions for Kirchhoff-type problems with critical growth in $\mathbb R^N$

Abstract

In this paper, we study the existence of infinitely many solutions for a class of Kirchhoff-type problems with critical growth in $\mathbb {R}^N$. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable positive parameters $\alpha , \beta $. The proofs are based on variational methods and the concentration-compactness principle.