Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

Abstract EN

We consider the existence of multiple solutions of the singular elliptic problem -div(|x|-ap|∇u|p-2∇u)+|u|p-2u/|x|(a+1)p=f|u|r-2u+h|u|s-2u+|x|-bp*|u|p*-2u, u(x)→0 as |x|→+∞, where x∈ℝN, 11, p*=Np/(N-pd), d=a+1-b.

By the variational method and the theory of genus, we prove that the above-mentioned problem has infinitely many solutions when some conditions are satisfied.