Existence of multiple positive weak solutions and estimates for extremal values to a class of elliptic problems with Hardy term and singular nonlinearity

This paper is devoted to the study of a class of elliptic equations of the form:−Δu−λ|x|2u=h(x)u−q+μW(x)up,x∈Ω\{0} with Dirichlet boundary conditions, where 0∈Ω⊂RN0∈Ω⊂RN (N≥3N≥3) is a bounded domain with smooth boundary ∂Ω, μ>0μ>0 is a parameter, 0<λ<Λ=(N−2)24, 00h(x)>0 and W(x)W(x) is a given function with the set {x∈Ω:W(x)>0}{x∈Ω:W(x)>0} of positive measure. Using variational methods, we establish some existence and multiplicity of positive solutions and provide uniform estimates of extremal values for the problem.