A Global Compactness Result And Positive Solutions For Sobolev-Hardy Equations

In this paper, we are concerned with the following Sobolev - Hardy Equations where whereΩis a bounded domain in R^N(N≥4), 0∈Ω, x = (y, z)∈Ω(?) R^k×R^h (?) R^N,2≤k < N,λ∈R,t∈(0,2), p(t) := (?) = 2^*(t) - 1 is Sobolev -Hardy exponent.Let (u_n)∈H₀¹(Ω) be a (P.S.) sequence of functional E_λ(u) = (?) We study the limit behavior of u_n and obtain a global compactness result,then we obtain positive solutions for the above problem by the Mountain Pass Lemma and the global compactness result.