EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponentwhere Ω (?) RN(N(?)3) is a smooth bounded domain, 0 ∈ Ω,0<s<p, 1<p< N,p (s) := p(N-s)/N-p is the critical Sobolev-Hardy exponent, λ> 0.p(?) r < p ,p’ := Np/N-p is the critical Sobolev exponent,μ> 0, 0(?)t < p,p(?)q < p (t) =p(N-t)/N-p. The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.