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.
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