Nonlinear differential equations with perturbed Dirichlet integral boundary conditions

Thumbnail Image

Files

2021_boundvalueprobl_cabada_nonlinear.pdf (1.52 MB)
Identifiers
URI: http://hdl.handle.net/10347/26779
E-ISSN: 1687-2770
DOI: 10.1186/s13661-021-01542-5

Publication date

2021

Authors

Advisors

Tutors

Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Springer
Metrics
Google Scholar
lacobus
Export

Research Projects

Organizational Units

Journal Issue

Abstract

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation of the Dirichlet conditions by considering a homogeneous Dirichlet-type condition at one extreme of the interval and an integral operator on the other one. We obtain the expression of the Green’s function related to the linear part of the equation and characterize its constant sign. Such a property will be fundamental to deduce the existence of solutions of the nonlinear problem. The results hold from fixed point theory applied to related operators defined on suitable cones

Description

Keywords

Integral boundary conditions| Green’s functions| Degree theory

Bibliographic citation

Bound Value Probl 2021, 66. https://doi.org/10.1186/s13661-021-01542-5

Relation

Has part

Has version

Is based on

Is part of

Is referenced by

Is version of

Requires

Sponsors

Alberto Cabada was partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER, grant MTM2016-75140-P

Rights

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/
Atribución 4.0 Internacional

Collections

Estatística, Análise Matemática e Optimización