Some global existence results on locally finite graphs

DOI10.1017/s1446788723000149MaRDI QIDQ6658025

Guoqing Zhang, Shoudong Man

Publication date: 8 January 2025

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Sobolev embedding theoremexistence of global solutionanalysis on graphdivision of a graph

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

• Harmonic functions of general graph Laplacians
• Kazdan-Warner equation on graph
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space
• Yamabe type equations on graphs
• Existence of positive solutions to some nonlinear equations on locally finite graphs
• Heat kernels on forms defined on a subgraph of a complete graph
• Existence of solution for a singular elliptic system with convection terms
• An elliptic nonlinear system of multiple functions with application
• The existence and nonexistence of global solutions for a semilinear heat equation on graphs
• Calculus of variations on locally finite graphs
• A 𝑝-th Yamabe equation on graph
• Ground state of semilinear elliptic systems with sum of periodic and Hardy potentials

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