Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Zhang, Xuechen, Zhang, Xingyong
Format: Preprint
Publié: 2024
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866914701187743744
author Zhang, Xuechen
Zhang, Xingyong
author_facet Zhang, Xuechen
Zhang, Xingyong
contents We investigate the existence of ground state solutions for a $(p,q)$-Laplacian system with $p,q>1$ and potential wells on a weighted locally finite graph $G=(V,E)$. By making use of the method of Nehari manifold and the Lagrange multiplier rule, we prove that if the nonlinear term $F$ takes on the super-$(p, q)$-linear growth and the potential functions $a(x)$ and $b(x)$ satisfy some suitable conditions, then for any fixed parameter $λ\geq1$, the system is provided with a ground state solution $(u_λ, v_λ)$. Additionally, we set up the convergence property of the solutions set $\{(u_λ, v_λ)\}$ when $λ\rightarrow +\infty$.
format Preprint
id arxiv_https___arxiv_org_abs_2403_02048
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs
Zhang, Xuechen
Zhang, Xingyong
Analysis of PDEs
We investigate the existence of ground state solutions for a $(p,q)$-Laplacian system with $p,q>1$ and potential wells on a weighted locally finite graph $G=(V,E)$. By making use of the method of Nehari manifold and the Lagrange multiplier rule, we prove that if the nonlinear term $F$ takes on the super-$(p, q)$-linear growth and the potential functions $a(x)$ and $b(x)$ satisfy some suitable conditions, then for any fixed parameter $λ\geq1$, the system is provided with a ground state solution $(u_λ, v_λ)$. Additionally, we set up the convergence property of the solutions set $\{(u_λ, v_λ)\}$ when $λ\rightarrow +\infty$.
title Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs
topic Analysis of PDEs
url https://arxiv.org/abs/2403.02048