Existence and multiplicity of positive solutions for a class of elliptic equations involving critical Sobolev exponents

Abstract

In this paper, we consider a class of elliptic equations involving critical Sobolev exponents. By the variational method and the Nehari method, we obtain the existence and multiplicity of positive solutions. We point out that the relation between the number of the maxima of the coefficient function of the critical term and the number of the positive solutions for the problem.