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

Part of: Boundary value problems Nonlinear integral equations Elliptic equations and systems

Published online by Cambridge University Press:  30 January 2019

Filomena Cianciaruso ,
Gennaro Infante  and
Paolamaria Pietramala
Filomena Cianciaruso
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy (cianciaruso@unical.it; gennaro.infante@unical.it; pietramala@unical.it)
Gennaro Infante
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy (cianciaruso@unical.it; gennaro.infante@unical.it; pietramala@unical.it)
Paolamaria Pietramala
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy (cianciaruso@unical.it; gennaro.infante@unical.it; pietramala@unical.it)
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Abstract

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.

Keywords

elliptic systemfixed point indexconenon-trivial solutionnonlinear functional boundary conditions

MSC classification

Primary: 35J66: Nonlinear boundary value problems for nonlinear elliptic equations
Secondary: 45G15: Systems of nonlinear integral equations 34B10: Nonlocal and multipoint boundary value problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 747 - 769
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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