The existence of positive solution for semilinear elliptic equations with multiple an inverse square potential and Hardy-Sobolev critical exponents. (English) Zbl 1474.35332

Summary: Via the concentration compactness principle, delicate energy estimates, the strong maximum principle, and the Mountain Pass lemma, the existence of positive solutions for a nonlinear PDE with multi-singular inverse square potentials and critical Sobolev-Hardy exponent is proved. This result extends several recent results on the topic.


35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35B50 Maximum principles in context of PDEs
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J75 Singular elliptic equations
35J60 Nonlinear elliptic equations
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