Mohammed El Mokhtar Ould El Mokhtar, Saleh Fahad Aljurbua
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引用次数: 0
摘要
本文试图建立具有符号变化权重、非线性奇异性和临界指数的奇异系统的非小解的存在性和多重性结果。通过使用变分法、Nehari 流形以及代表一些物理意义的参数 η 的充分条件,我们证明了一些现有结果,即在参数 α、β、μ 和 η 的一些充分条件下,研究临界点作为与 Nehari 流形定义的约束上所提问题 (2) 相关的能量函数的最小值,这些临界点就是我们系统的解。据我们所知,本文是对具有符号变化权重、非线性奇异性和临界指数的奇异系统研究的首次贡献之一。
Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent
This paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent. By using variational methods, the Nehari manifold, and under sufficient conditions on the parameter η which represent some physical meanings, we prove some existing results by researching the critical points as the minimizers of the energy functional associated with the proposed problem (2) on the constraint defined by the Nehari manifold, which are solutions of our system, under some sufficient conditions on the parameters α, β, μ, and η. To the best of our knowledge, this paper is one of the first contributions to the study of singular systems with sign-changing weight, nonlinear singularities, and critical exponent.
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.