Existence of Homoclinic Solutions for a Class of Nonlinear Second-order Problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-19 DOI:10.1007/s12346-024-01114-9

Wei Yang, Ruyun Ma

引用次数: 0

Abstract

We are concerned with the existence of homoclinic solutions for the nonlinear problems

$$\begin{aligned} \left\{ \begin{array}{ll} u''+\omega u'-ku=f(t,u,u'),\ \ t\in \mathbb {R},\\ \lim \limits _{|t|\rightarrow +\infty }u(t)=0, \end{array} \right. \end{aligned}$$(P)

where $\omega \in \mathbb {R},~k>0$ are real constants, and $f: \mathbb {R}^{3}\rightarrow \mathbb {R}$ is an $L^{1}-$Carathéodory function. Under some suitable conditions, the existence of homoclinic solutions for problem (P) and the corresponding coupled systems are provided. The proofs of the main results are based on the method of upper and lower solutions.

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一类非线性二阶问题的同线性解的存在性

我们关注的是非线性问题 $$\begin{aligned} 的同轴解的存在性\u'-ku=f(t,u,u'),tin mathbb {R},limlimits _{|t|rightarrow +\infty }u(t)=0, end{array}\right.\end{aligned}$$(P)where $\omega \in \mathbb {R},~k>0$ are real constants, and $f: \mathbb {R}^{3}\rightarrow \mathbb {R}$ is an $L^{1}-$Carathéodory function.在一些合适的条件下，提供了问题（P）和相应耦合系统的同轴解的存在性。主要结果的证明基于上解和下解的方法。

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.

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