Existence of solutions to biharmonic systems with singular nonlinearity

Abstract

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.

Keywords

• Biharmonic operator
• singular nonlinearity
• Green function
• Schauder's fixed point theorem