Existence Of Multiple Positivae Solutions For Singular Elliptic Equation Involving Hardy-Sobolev-Maz'ya Term

In this paper, we study the existence of multiple positive solutions of the sin-gular semilinear elliptic equation involving Hardy—Sobolev—Maz' ya inequality in a bounded domain in RN, where x∈RN is denoted as x=(y, z)∈Rk×x Rn-k and Ifκ= 2,λ=0; 0≤t< 2, f(x) is a smooth function, f(x)> 0 and f(x)(?)0. In this paper, we prove that there exists a positive constantμ* such that for allμ∈(0,μ*), the problem has at least two positive solutions. To approach this, First, we use the method of subsolutions and supersolutions to prove that the problem possesses a minimal solution, Then we use the Mountain pass theorem for the second positive solution.