Multiple solutions for a boundary singular semilinear equation with sublinear term involving Hardy potential and Hardy-Sobolev Exponent. (English) Zbl 1526.35179
Summary: In this paper we establish the existence of at least two solutions to a singular elliptic equations with zero boundary data and critical Hardy-Sobolev exponent. We show that the existence of the positive solution in high dimension depends on the sign of the mean curvature of the boundary near zero and in the low dimensions its depends of sign of the mass of the domain.
MSC:
| 35J75 | Singular elliptic equations |
| 35J61 | Semilinear elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
semi-linear singular elliptic equation; critical Hardy-Sobolev exponent; Dirichlet condition; existenceReferences:
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