Quasilinear elliptic problems with critical exponents and Hardy terms Original Research Article

Let Ω∋0Ω∋0 be an open bounded domain, Ω⊂RN(N>p2)Ω⊂RN(N>p2). We are concerned with the multiplicity of positive solutions of View the MathML source-Δpu-μ|u|p-2u|x|p=λ|u|p-2u+Q(x)|u|p*-2u,u∈W01,p(Ω), Turn MathJax on where View the MathML source-Δpu=-div(|∇u|p-2∇u),10 Turn MathJax on and Q(x)Q(x) is a nonnegative function on View the MathML sourceΩ¯. By investigating the effect of the coefficient of the critical nonlinearity, we, by means of variational method, prove the existence of multiple positive solutions.