Multiple Solutions for a Variable-Order p(x,·)-Kirchhoff-Type Problem With Weight

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-26 DOI:10.1002/mma.10808

E. Azroul, N. Kamali, M. Shimi

引用次数: 0

Abstract

In this study, we establish the existence of three weak solutions for a Kirchhoff-type problem with weight that involves the variable-order $p (x, \cdot)$ -Laplacian operator. We introduce a suitable functional framework for addressing such problems and establish a fundamental continuous and compact embedding theorem of this framework. Using Ricceri's three critical point approach, we prove the existence of weak solutions in the context of weighted variable-order Sobolev spaces with variable exponents.

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一类带权变阶p（x，·）- kirchhoff型问题的多重解

在本研究中，我们建立了涉及变阶p （x，·）$$ p\left(x,\cdotp \right) $$ -拉普拉斯算子的权重kirchhoff型问题的三个弱解的存在性。我们引入了一个合适的函数框架来解决这类问题，并建立了该框架的基本连续紧嵌入定理。利用Ricceri的三临界点方法，证明了变指数加权变阶Sobolev空间弱解的存在性。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.