Existence of positive solutions for a class of degenerate or singular equations Original Research Article

In this paper, we consider the class of equations View the MathML source−div(|x|−2a∇u)=A|x|2(α+a)u+uθ|x|bp,x∈Rn∖{0}. Turn MathJax on where a,b∈R,n>2,A∈Ra,b∈R,n>2,A∈R, α>0α>0 and View the MathML sourceθ>0,p=2nn−2(1+a−b). In various range of the parameters involved, we obtain both results of existence and nonexistence of positive solutions by combining the Mountain Pass Lemma and the Pohozaev-type identity.