Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs

2024/01/27 by Pang, Yan, Xie, Junping, Zhang, Xingyong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.15372

Abstract

We investigate a generalized poly-Laplacian system with a parameter on weighted finite graph, 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. 2010, 52(1-2): 152-160], which is an abstract critical points theorem without compactness condition, to obtain that these three systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range.

Cited by

• Infinitely many solutions for a biharmonic-Kirchhoff system on locally finite graphs

Related

• Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs
• Dependence on parameters of solutions for a generalized poly-Laplacian system on weighted graphs
• Existence of three solutions for a poly-Laplacian system on graphs
• Nontrivial solutions for a generalized poly-Laplacian system on finite graphs
• Existence and multiplicity of nontrivial solutions for a (p,q)-Laplacian system on locally finite graphs