Existence of solutions to discrete and continuous second-order boundary value problems via Lyapunov functions and a priori bounds

Tisdell, Christopher C. and Liu, Yongjian and Liu, Zhenhai: Existence of solutions to discrete and continuous second-order boundary value problems via Lyapunov functions and a priori bounds. Electronic journal of qualitative theory of differential equations 42. pp. 1-11. (2019)

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Abstract

This article analyzes nonlinear, second-order difference equations subject to “left-focal” two-point boundary conditions. Our research questions are: RQ1: What are new, sufficient conditions under which solutions to our “discrete” problem will exist?; RQ2: What, if any, is the relationship between solutions to the discrete problem and solutions of the “continuous”, left-focal analogue involving second-order ordinary differential equations? Our approach involves obtaining new a priori bounds on solutions to the discrete problem, with the bounds being independent of the step size. We then apply these bounds, through the use of topological degree theory, to yield the existence of at least one solution to the discrete problem. Lastly, we show that solutions to the discrete problem will converge to solutions of the continuous problem.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 42
Page Range: pp. 1-11
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.42
Uncontrolled Keywords: Differenciálegyenlet - határérték probléma
Additional Information: Bibliogr.: p. 9-11. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 27. 13:40
Last Modified: 2019. Sep. 27. 13:40
URI: http://acta.bibl.u-szeged.hu/id/eprint/62120

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