加权图上三个准线性拉普拉斯系统的无限多解

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-03-28 DOI:10.1186/s13661-024-01846-2

Yan Pang, Junping Xie, Xingyong Zhang

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引用次数: 0

摘要

我们研究了加权有限图上带参数的广义多拉普拉斯系统、加权局部有限图上带参数和迪里希特边界值的广义多拉普拉斯系统以及加权局部有限图上带参数的 $(p,q)$ 拉普拉斯系统。我们利用 Bonanno 和 Bisci [Bonanno, Bisci, and Regan, Math. Comput. Model. 52(1-2):152-160, 2010] 建立的临界点定理（这是一个没有紧凑性条件的抽象临界点定理），得出当参数位于某个确定的范围内时，这些系统具有无限多的无约束规范的非微观解。

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Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs

We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a $(p,q)$ -Laplacian system with a parameter on weighted locally finite graphs. We utilize a critical points theorem built by Bonanno and Bisci [Bonanno, Bisci, and Regan, Math. Comput. Model. 52(1-2):152–160, 2010], which is an abstract critical points theorem without compactness condition, to obtain that these systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.