Existence and multiplicity of solutions for a superlinear Kirchhoff-type equations with critical Sobolev exponent in [formula omitted

Abstract

In this article, we consider a class of superlinear Kirchhoff-type equations with critical growth {−(a+b∫RN∣∇u∣2dx)Δu=μu2∗−1+λk(x)uq−1,x∈RN,u∈D1,2(RN), where λ,μ>0,N≥4,2≤q<2∗,2∗=2NN−2,a,b≥0 and a+b>0,k satisfies some conditions. By using the variational method, the multiplicity of positive solutions and infinitely many pairs of solutions are obtained.