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 non-negative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem

“…Our results are new and complement previous results of the author [24], by allowing the presence of gradient terms within the nonlinearities and the functionals. The results also complement the ones in [4], by considering more general nonlocal elliptic systems.…”