On some differential equations involving a new kind of variable exponents

IF 1.1 4区 数学 Q1 MATHEMATICS
S. Aouaoui
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引用次数: 2

Abstract

In this paper, we are concerned with some new first order differential equation defined on the whole real axis R . The principal part of the equation involves an operator with variable exponent p depending on the variable x ∈ R through the unknown solution while the nonlinear part involves the classical variable exponent p ( x ) . Such kind of situation is very related to the presence of the variable exponent and has not been treated before. Our existence result of nontrivial solution cannot be reached using standard variational or topological methods of nonlinear analysis and some sophisticated arguments have to be employed.
关于一类新的变指数微分方程
本文讨论了在整个实轴R上定义的一类新的一阶微分方程。方程的主要部分涉及一个变量指数p的算子,它依赖于变量x∈R通过未知解,而非线性部分涉及经典变量指数p (x)。这种情况与变指数的存在有很大关系,以前没有处理过。我们的非平凡解的存在性结果不能用标准的变分方法或拓扑方法得到,必须采用一些复杂的论证。
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
CiteScore
1.40
自引率
9.10%
发文量
23
审稿时长
3 months
期刊介绍: The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.
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