Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in RN

We consider asymptotic behavior for a parabolic equation (p-heat equation) with (sub-)critical Sobolev and Hardy exponent potential ut−div(|∇u|p−2∇u)+f(u)=V(x)|u|q−2|x|su,where 1λN,p,λ<λN,p. By using the standard domain expansion technique and some convenient integrability conditions on the weighted function V(x), we first establish that the Cauchy problem has at least one global solution for every 1