Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains

Abstract

We prove new results on the existence, non-existence, localization and multiplicity of nontrivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to nonlocal, nonlinear, functional boundary conditions. Our approach relies on fixed point index theory. As a by-product of our theory we provide an answer to an open question posed by do {Ó}, Lorca, Sánchez and Ubilla. We include some examples with explicit nonlinearities in order to illustrate our theory.

24 pages

References in corpus (3)

• Solutions of perturbed Hammerstein integral equations with applications
• Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains
• Non-trivial solutions of local and non-local Neumann boundary-value problems

Cited by in corpus (2)

• Nonzero positive solutions of elliptic systems with gradient dependence and functional BCs
• Asymptotic properties of PDEs in compact spaces