Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs

Fuente: arXiv
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Hauptverfasser: Yu, Zhangyi, Xie, Junping, Zhang, Xingyong, Qi, Wanting
Format: Preprint
Veröffentlicht: 2024
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author Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
Qi, Wanting
author_facet Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
Qi, Wanting
contents We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the variational methods which are based on mountain pass theorem and topological degree theory. We obtain that these two systems have a sequence of minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional $φ(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional $φ(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$.
format Preprint
id arxiv_https___arxiv_org_abs_2404_08272
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs
Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
Qi, Wanting
Analysis of PDEs
We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the variational methods which are based on mountain pass theorem and topological degree theory. We obtain that these two systems have a sequence of minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional $φ(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional $φ(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$.
title Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs
topic Analysis of PDEs
url https://arxiv.org/abs/2404.08272