Infinitely of solutions for fractional κ(ξ)-Kirchhoff equation in Hκ(ξ)ϖνμ(Λ)

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-09-16 DOI:10.1002/mma.10477

Abdelhakim Sahbani, J. Vanterler da C. Sousa

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Abstract

This work aims to develop the variational framework for some Kirchhoff problems involving the $μ$ -Hilfer operator. Precisely, we use the symmetric mountain pass theorem to prove the existence of unfairly of nontrivial solutions. Further, we research the results from the theory of variable exponent Sobolev spaces and from the theory of $μ$ -fractional space $H_{κ (ξ)}^{ϖ, ν; μ} (Λ)$ .

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在Hκ(ξ)ϖ,ν中的分式κ(ξ)$$ {{kappa（左）（西）（右）}$$-基尔霍夫方程的无限解μ（Λ）$$ {{mathcal{H}}_{kappa（左）（西）（右）}^{\varpi, \nu;\mu}（左）（λ）$$

这项工作旨在为一些涉及 -Hilfer 算子的基尔霍夫问题建立变分框架。确切地说，我们利用对称山口定理证明了非小解的不公平存在。此外，我们还研究了变指数索波列夫空间理论和-分数空间理论的成果。

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.