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We prove new results on the existence, non-existence, localization and multiplicity of non-trivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to non-local, 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.

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

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Non-Zero Radial Solutions for Elliptic Systems with Coupled Functional BCs in Exterior Domains

Non-trivial solutions of local and non-local Neumann boundary-value problems

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Non-Zero Radial Solutions for Elliptic Systems with Coupled Functional BCs in Exterior Domains

Non-trivial solutions of local and non-local Neumann boundary-value problems