Multiple positive solutions for a critical growth problem with hardy potential

Abstract

In this paper we study the existence and nonexistence of multiple positive solutions for the Dirichlet problem: equation presented where equation presented. Using the sub-supersolution method and the variational approach, we prove that there exists a positive number λ* such that problem (*) possesses at least two positive solutions if λ ∈ (0,λ*), a unique positive solution if λ = λ* and no positive solution if λ ∈ (λ*, ∞).