Positive solutions of BVPs on the half-line involving functional BCs

Gennaro Infante; Serena Matucci; Gennaro Infante; Serena Matucci

doi:10.3934/math.2021285

AIMS Mathematics

2021, Volume 6, Issue 5: 4860-4872. doi: 10.3934/math.2021285

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Positive solutions of BVPs on the half-line involving functional BCs

Gennaro Infante ^{1
,
,},
Serena Matucci ²

1.
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy
2.
Department of Mathematics and Computer Science "Ulisse Dini", University of Florence, 50139 Florence, Italy

Received: 29 December 2020 Accepted: 17 February 2021 Published: 26 February 2021
MSC : Primary 34B40; secondary 34B10, 34B18

We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on compact intervals, a fixed point result for operators on noncompact sets, and some comparison results for principal and nonprincipal solutions of suitable auxiliary linear equations.
- fixed point index,
- cone,
- positive global solution,
- functional boundary condition
Citation: Gennaro Infante, Serena Matucci. Positive solutions of BVPs on the half-line involving functional BCs[J]. AIMS Mathematics, 2021, 6(5): 4860-4872. doi: 10.3934/math.2021285

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Abstract

We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on compact intervals, a fixed point result for operators on noncompact sets, and some comparison results for principal and nonprincipal solutions of suitable auxiliary linear equations.

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