EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

doi:10.1016/S0252-9602(17)30047-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 911-926.doi: 10.1016/S0252-9602(17)30047-4

EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

Alberto CABADA¹, Nikolay D. DIMITROV²

1. Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain;
2. Department of Mathematical Analysis, University of Rousse, 7017 Rousse, Bulgaria

收稿日期:2016-04-14 出版日期:2017-08-25 发布日期:2017-08-25
作者简介:Alberto CABADA,E-mail:alberto.cabada@usc.es;Nikolay D.DIMITROV,E-mail:ndimitrov@uni-ruse.bg

EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

Alberto CABADA¹, Nikolay D. DIMITROV²

1. Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain;
2. Department of Mathematical Analysis, University of Rousse, 7017 Rousse, Bulgaria

Received:2016-04-14 Online:2017-08-25 Published:2017-08-25
About author:Alberto CABADA,E-mail:alberto.cabada@usc.es;Nikolay D.DIMITROV,E-mail:ndimitrov@uni-ruse.bg

摘要/Abstract

摘要：

This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

关键词: Dirichlet boundary value problem, nonlocal perturbations, Green's function, parameter dependence

Abstract:

Key words: Dirichlet boundary value problem, nonlocal perturbations, Green's function, parameter dependence

Alberto CABADA, Nikolay D. DIMITROV. EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS[J]. 数学物理学报(英文版), 2017, 37(4): 911-926.

Alberto CABADA, Nikolay D. DIMITROV. EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS[J]. Acta mathematica scientia,Series B, 2017, 37(4): 911-926.

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EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

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