Well Ordered Monotone iterative Technique for nonlinear second order Four Point Dirichlet BVPs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-02-07 DOI:10.3846/mma.2022.14198

Amit Verma, Nazia Urus

引用次数: 3

Abstract

In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as, ... where ..., ... the non linear term ...is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution and upper solution such that... Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where

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非线性二阶四点Dirichlet BVPs的良序单调迭代技术

在本文中，我们发展了一类四点Dirichlet非线性边值问题(NLBVPs)的具有上下(L-U)解的单调迭代技术(mi -技术)，定义为，…在那里……,……非线性项。是在x中的连续函数，在ψ中的单侧Lipschitz和。为了证明存在性，我们构造了相应线性问题的格林函数和迭代序列。我们使用拟线性化来构造这些迭代格式。证明了极大值原理，建立了下解和上解序列的单调性。然后在一定的充分条件下，证明了这些序列在一个特定的区域内一致收敛于ψ(x)的解

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.