Solutions to discrete nonlinear Kirchhoff-Choquard equations

2024/04/18 by Wang, Lidan · 2 citations
#35J20 #35R02 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.11856

Abstract

In this paper, we study the discrete Kirchhoff-Choquard equation -(a+b ∫_ℤ³|∇ u|² d μ) Δu+V(x) u=(R_α *F(u))f(u), x∈ ℤ³, where a, b>0 are constants, R_α is the Green's function of the discrete fractional Laplacian with α∈(0,3), which has no singularity but has same asymptotics as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions by variational methods.

Cited by

• Positive solutions to fractional p-Laplacian Choquard equation on lattice graphs
• Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs

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