Electron. J. Diff. Equ., Vol. 2016 (2016), No. 177, pp. 1-12.

Existence of solutions to biharmonic systems with singular nonlinearity

Anderson L. A. de Araujo, Luiz F. O. Faria

In this article we prove the existence of positive solutions of nonlinear singular biharmonic elliptic systems in smooth bounded domains, with coupling of the equations, under Navier boundary condition. Under some suitable assumptions on the nonlinearity, we prove a uniqueness result. The existence result is based on the Schauder's fixed point theorem.

Submitted March 22, 2016. Published July 6, 2016.
Math Subject Classifications: 35B09, 35B45, 35J58, 35J75.
Key Words: Biharmonic operator; singular nonlinearity; Green function; Schauder's fixed point theorem.

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Anderson L. A. de Araujo
Departamento de Matem´tica
Universidade Federal de Viçosa
CEP 36570-900 Viçosa
Minas Gerais, Brazil
email: anderson.araujo@ufv.br
Luiz F. O. Faria
Departamento de Matem´tica - ICE
Universidade Federal de Juiz de Fora
CEP 36036-330 Juiz de Fora
Minas Gerais, Brazil
email: luiz.faria@ufjf.edu.br

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