Existence and uniqueness of positive solution for discrete multipoint boundary value problems
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive solution for discrete multipoint boundary value problems
zbMATH Open document ID: 1490.39004
DOI: 10.1155/2014/531978
author: Huili Ma
author: Huifang Ma
published in: International Scholarly Research Notices. Mathematical Analysis
publication date: 2019-02-21T00:00:00Z
review text: Summary: It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: \(- \Delta^2 u(t - 1) = f(t, u(t)) + g(t, u(t))\), \(t \in \mathbb{Z}_{1, T}\), subject to boundary conditions either \(u(0) - \beta \Delta u(0) = 0\), \(u(T + 1) = \alpha u(\eta)\) or \(\Delta u(0) = 0\), \(u(T + 1) = \alpha u(\eta)\), where \(0 < \alpha < 1\), \(\beta > 0\), and \(\eta \in \mathbb{Z}_{2, T - 1}\). The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 7027197
Wikidata QID: Q36979895
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/531978
OpenAlex ID: W2084145462
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description: scientific article; zbMATH DE number 7027197