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Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs

Authors
  • Biagi, Stefano1
  • Calamai, Alessandro2
  • Infante, Gennaro3
  • 1 Politecnico di Milano, Via Bonardi 9, 20133 , (Italy)
  • 2 Università Politecnica delle Marche, Via Brecce Bianche, 60131 , (Italy)
  • 3 Università della Calabria, 87036 Arcavacata di Rende , (Italy)
Type
Published Article
Journal
Advanced Nonlinear Studies
Publisher
De Gruyter
Publication Date
Aug 06, 2020
Volume
20
Issue
4
Pages
911–931
Identifiers
DOI: 10.1515/ans-2020-2101
Source
De Gruyter
Keywords
License
Green

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 nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

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