Positive homoclinic solutions of n-th order difference equations with sign-changing Green's function

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MMAS-Cabada-Dimitrov-2018.pdf (230.7 KB)
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URI: https://hdl.handle.net/10347/44937
ISSN: 0170-4214
E-ISSN: 1099-1476
DOI: 10.1002/mma.4929

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2018-04-16

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Wiley
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Abstract

In this paper we, consider an n-th order nonlinear difference equation with parameter dependence. An exhaustive study of the related Green's function is done. The exact expression of the function is given. The range of parameter for which either it has constant sign or it changes sign is obtained. Some existence results for the nonlinear problem are deduced by using the classical Krasnosel'skii's fixed point theorem on cones and fixed point index theory.

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This is the peer reviewed version of the following article: [Cabada A, Dimitrov ND. Positive homoclinic solutions of n-th order difference equations with sign-changing Green's function. Math Meth Appl Sci. 2018; 41: 4763–4775], which has been published in final form at [https://doi.org/10.1002/mma.4929]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.

Keywords

Difference equation| Homoclinic solutions| Positive solutions| Parameter dependence| Sign-changing Green's function

Bibliographic citation

Cabada A, Dimitrov ND. Positive homoclinic solutions of n-th order difference equations with sign-changing Green's function. Math Meth Appl Sci. 2018; 41: 4763–4775. https://doi.org/10.1002/mma.4929

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First author was partially supported by AIE Spain and FEDER, grants MTM2013-43014-P, MTM2016-75140-P. The second author is supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution,” 2017.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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Estatística, Análise Matemática e Optimización
Instituto de Matemáticas