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.

References in corpus (6)

• Solutions of perturbed Hammerstein integral equations with applications
• Nonzero positive solutions of nonlocal elliptic systems with functional BCs
• Green's function for second order elliptic equations with singular lower order coefficients
• Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains
• Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence
• Nonzero positive solutions of a multi-parameter elliptic system with functional BCs

Cited by in corpus (3)

• Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem
• A Unified Topological Analysis of Variable Growth Kirchhoff-Type Equations
• On the solvability of parameter-dependent elliptic functional BVPs on annular-like domains