Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term

Abstract

In this paper, a class of Kirchhoff type equations in ℝN (N ⩾ 3) with zero mass and a critical term is studied. Under some appropriate conditions, the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem. The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem. Compared to the usual Kirchhoff-type problems, we only require the nonlinearity to satisfy the classical superquadratic condition (Ambrosetti-Rabinowitz condition).