Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent

In this paper, we consider the following Kirchhoff-type problems involving critical exponent backward. The existence and multiplicity of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth are studied under some suitable assumptions on V By using the mountain pass theorem and Brezis-Lieb lemma, the existence and multiplicity of positive solutions are obtained.