Non-Zero Radial Solutions for Elliptic Systems with Coupled Functional BCs in Exterior Domains. Issue 3 (30th January 2019)

• Record Type: Journal Article
• Authors: Cianciaruso, Filomena; Infante, Gennaro; Pietramala, Paolamaria
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 3(2019)
• Page Start: 747
• Page End: 769
• Publication Date: 2019-01-30
• Subjects: elliptic system, -- fixed point index, -- cone, -- non-trivial solution, -- nonlinear functional boundary conditions; Primary 35J66, -- Secondary 45G15, -- 34B10; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091518000706
• Languages: English
• ISSNs: 0013-0915

Abstract

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.