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Existence and uniqueness of positive solutions for singular biharmonic elliptic systems. (English) Zbl 1342.35103

Summary: In this paper we prove existence and uniqueness of positive solutions of nonlinear singular biharmonic elliptic systems in smooth bounded domains, with coupling of the equations, under Navier boundary condition. The solution is constructed through an approximating process based on a priori estimates, regularity up to the boundary and Hardy-Sobolev inequality.

MSC:

35J58 Boundary value problems for higher-order elliptic systems
35B09 Positive solutions to PDEs
35B45 A priori estimates in context of PDEs
35J75 Singular elliptic equations
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