Positive solutions to fractional p-Laplacian Choquard equation on lattice graphs

2025/07/30 by Wang, Lidan
#35A15 #35R02 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.22552

Abstract

In this paper, we study the fractional p-Laplacian Choquard equation (-Δ)_p^s u+h(x)|u|^p-2 u=(R_α *F(u))f(u) on lattice graphs ℤ^d, where s∈(0,1), p≥ 2, α∈(0, d) and R_α represents the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under suitable assumptions on the potential function h, we first prove the existence of a strictly positive solution by the mountain-pass theorem for the nonlinearity f satisfying some growth conditions. Moreover, if we add some monotonicity condition, we establish the existence of a positive ground state solution by the method of Nehari manifold.

Citations

• Fractional Sobolev spaces and fractional p-Laplace equations on locally finite graphs
• p-Laplacian equations with general Choquard nonlinearity on lattice graphs
• Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity
• Fractional Laplace operator and related Schrödinger equations on locally finite graphs
• Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations
• Solutions to discrete nonlinear Kirchhoff-Choquard equations
• Solutions to discrete fractional Schödinger equations
• Sobolev spaces on locally finite graphs
• Eigenvalue estimates for the fractional Laplacian on lattice subgraphs
• Normalized solutions for nonlinear Schrödinger equations on graphs
• The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth
• The existence of positive ground state solutions for the Choquard type equation on groups of polynomial growth
• Calculus of variations on locally finite graphs
• Nodal solutions for the Choquard equation
• Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics

Related

• p-Laplacian equations with general Choquard nonlinearity on lattice graphs
• Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs
• The existence of positive ground state solutions for the Choquard type equation on groups of polynomial growth
• The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth
• Ground state solutions of p-Laplacian equations with nonnegative potentials on Lattice graphs