Positive solutions of a general discrete Dirichlet boundary value problem
type: Item
instance of: scholarly article
title: Positive solutions of a general discrete Dirichlet boundary value problem
zbMATH Open document ID: 1417.39028
DOI: 10.1155/2016/7456937
author: Xinfu Li
author: Guang Zhang
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on any \(n\)-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.
Mathematics Subject Classification ID: 39A14
zbMATH DE Number: 7025603
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7456937
OpenAlex ID: W2292632316
Wikidata QID: Q59123640
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description: scientific article; zbMATH DE number 7025603