Existence of three solutions for a poly-Laplacian system on graphs

2023/09/18 by Yan Pang, Xingyong Zhang, Pang, Yan +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.09849

openalex publication_date 2023/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a (p,q)-Laplacian system with a parameter on locally finite graphs.The main tool is an abstract critical points theorem in [Bonanno and Bisci, J.Math.Appl.Anal, 2011, 382(1): 1-8]. A key point in this paper is that we overcome the difficulty to prove that the Gateaux derivative of the variational functional for poly-Laplacian operator admits a continuous inverse, which is caused by the special definition of the poly-Laplacian operator on graph and mutual coupling of two variables in system.

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