Existence and Multiplicity of Homoclinic Solutions for ϕ-Laplacian Parametric Partial Difference Equations

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-25 DOI:10.1002/mma.11172

Yuhua Long, Sha Li

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引用次数: 0

Abstract

By means of the Ekeland variational principle coupled with the mountain pass lemma, we study a class of nonlinear second-order parametric partial difference equations involving $ϕ_{c}$ -Laplacian. Taking into account both the cases of large $λ$ and small $λ$ , we establish criteria to ensure the existence of two nontrivial homoclinic solutions for sufficiently large $λ$ and one nontrivial homoclinic solution for all $λ > 0$ . Finally, three special examples are presented to demonstrate the applications of our results. Our assumptions relax some known ones, and results generalize some existing literature.

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参数偏差分方程的同斜解的存在性和多重性

利用Ekeland变分原理结合山口引理，研究了一类包含ϕ - c $$ {\phi}_c $$ -拉普拉斯算子的非线性二阶参数偏差分方程。考虑到大λ $$ \lambda $$和小λ $$ \lambda $$的情况，建立了足够大λ $$ \lambda $$的两个非平凡同斜解的存在性准则和所有λ ＆gt； 0 $$ \lambda &gt;0 $$的一个非平凡同斜解的存在性准则。最后，给出了三个特殊的例子来说明我们的结果的应用。我们的假设放宽了一些已知的假设，结果推广了一些现有的文献。

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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.