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

2024/03/04 by Zhang, Xuechen, Zhang, Xingyong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.02048

Abstract

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≥1, 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→ +∞.

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• Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs

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