Coupled elliptic systems depending on the gradient with nonlocal BCs in exterior domains

Abstract

We study existence and multiplicity of positive radial solutions for a coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the boundary conditions are nonlocal. We use a nonstandard cone to establish existence of solutions by means of fixed point index theory.Many papers are aimed to the existence of radial solutions of elliptic equations in the exterior part of a ball. A variety of methods has been used, for instance, when the boundary conditions (BCs) are homogeneous, a priori estimates were utilized by Castro et al. [7], sub and super solutions were used by Djedali and Orpel [16]