Positive And Sign-Changing Solutions For The Singular Elliptic Equation Involving Hardy-Sobolev-Maz'ya Terms

In this paper,we study the existence of positive solutions and sign-changing solutions of the singular semilinear elliptic equation involving Hardy-Sobolev-Maz'ya terms in a bounded domainΩwith smooth boundary where x=(y,z)∈Rk×RN-k,2≤k＜N,pt=(N+2-2t)/(N-2),0≤t＜2.Moreover,0≤λ＜((k-2)2)/4,0＜μ＜λ1(λ),λ1(λ)is the first cigenvalue of operator一△一λ/|y|2.This paper studies the case of it meansTo prove the existence of positive solutions,we use the global compact-ness theorem and the Mountain pass theorem；to approach the existence of sign-changing solutions,we use the dual theory.