Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN

In this work we study the existence and multiplicity of solutions to the following Kirchhoff-type problem with critical nonlinearity in RN−a+b∫RN∇updxΔpu=μup∗−1+λf(x,u);x∈RN,u∈D1,p(RN),where N≥2p, μ,λ,a,b>0 and the nonlinearity f(x,u) satisfies certain subcritical growth conditions. By using topological and variational methods, infinitely many positive solutions are obtained.