EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

doi:10.1007/s10473-020-0115-y

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 226-236.doi: 10.1007/s10473-020-0115-y

EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

Alberto CABADA¹, Nikolay DIMITROV²

1. Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain;
2. Depatment of Mathematics, University of Ruse, Ruse 7000, Bulgaria

收稿日期:2018-09-27 修回日期:2019-05-09 出版日期:2020-02-25 发布日期:2020-04-14
基金资助:
First author was partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER, grant MTM2016-75140-P. The second author was supported by the Bulgarian National Science Fundation under Project DN 12/4 "Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution", 2017.

EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

Alberto CABADA¹, Nikolay DIMITROV²

1. Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain;
2. Depatment of Mathematics, University of Ruse, Ruse 7000, Bulgaria

Received:2018-09-27 Revised:2019-05-09 Online:2020-02-25 Published:2020-04-14
Supported by:
First author was partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER, grant MTM2016-75140-P. The second author was supported by the Bulgarian National Science Fundation under Project DN 12/4 "Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution", 2017.

摘要/Abstract

摘要： The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.

关键词: difference equation, multiplicity of solutions, Green's function, positive solutions, parameter dependence

Abstract: The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.

Key words: difference equation, multiplicity of solutions, Green's function, positive solutions, parameter dependence

中图分类号:

39A10

Alberto CABADA, Nikolay DIMITROV. EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2020, 40(1): 226-236.

Alberto CABADA, Nikolay DIMITROV. EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2020, 40(1): 226-236.

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EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

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