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This study with Hardy - Sobolev - Maz'ya items singular semilinear elliptic equations in a bounded domain with smooth boundary omega ( ? ) RN on the existence of multiple positive solutions , where x = ( y , z ) ∈ Rk × RN-k, 2 ≤ k lt; N when k GT ; 2 , when k = 2 , lambda = 0 ; mu GT ; 0 for the parameter , f ( x ) is a smooth function , f ( x ) ≥ 0 , and f ( x ) = 0 In this paper, we prove : there is a normal number of mu * such that for any mu ∈ ( 0 , mu * ) , the existence of at least two positive solutions first, we use the upper and lower solution method to prove the existence of at least a very small positive solution, and then , using mountain pass theorem to prove the existence of positive solutions .
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