Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs

Abstract

We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

Keywords

• positive solution
• elliptic system
• gradient terms
• functional boundary condition
• cone
• fixed point index
• 35j47
• 35b09
• 35j57
• 35j60
• 47h10