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

摘要

In this paper, we consider the following Kirchhoff-type problems involving critical exponent ?a+b∫Ω?u2dxΔu+Vxu=μu2??1+λgx,u,?x∈Ωu0,?x∈Ωu=0,?x∈?Ω. 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 Vx and gx,u. By using the mountain pass theorem and Brézis–Lieb lemma, the existence and multiplicity of positive solutions are obtained.