Existence and uniqueness of positive solutions for singular biharmonic elliptic systems

Luiz F. O.  Faria

doi:10.3934/proc.2015.0400

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2015, Volume 2015: 400-408. Doi: 10.3934/proc.2015.0400 open access

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Existence and uniqueness of positive solutions for singular biharmonic elliptic systems

Luiz F. O. Faria^1,

1.
Departamento de Matemática - ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, CEP 36036-330, Minas Gerais

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

In this paper we prove existence and uniqueness of positive solutions of nonlinear singular biharmonic elliptic system 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.

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Mathematics Subject Classification: 35B09, 35B45, 35J58, 35J75.

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