Existence and multiplicity of nontrivial solutions for poly-Laplacian systems on finite graphs

DOI10.1186/s13661-022-01613-1zbMath1497.35262OpenAlexW4281747594MaRDI QIDQ2153876

Xuechen Zhang, Junping Xie, Xiao-li Yu, Xing-Yong Zhang

Publication date: 13 July 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-022-01613-1

zbMATH Keywords

mountain pass theorempoly-Laplacian system on finite graphs

Mathematics Subject Classification ID

Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Boundary value problems for second-order elliptic systems (35J57) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (1)

Existence of nontrivial solutions for a poly-Laplacian system involving concave-convex nonlinearities on locally finite graphs

Cites Work

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• Existence of nonconstant periodic solutions for a nonlinear discrete system involving the \(p\)-Laplacian
• Yamabe equations on infinite graphs
• Yamabe type equations on graphs
• Positive solutions of \(p\)-th Yamabe type equations on graphs
• \(p\)-Laplacian equations on locally finite graphs
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• A 𝑝-th Yamabe equation on graph
• Positive solutions of $p$-th Yamabe type equations on infinite graphs

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