Existence of three solutions for a poly-Laplacian system on graphs
Analysis of PDEs
2023-09-19 v1
Abstract
We deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a -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 Gteaux 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.
Keywords
Cite
@article{arxiv.2309.09849,
title = {Existence of three solutions for a poly-Laplacian system on graphs},
author = {Yan Pang and Xingyong Zhang},
journal= {arXiv preprint arXiv:2309.09849},
year = {2023}
}