Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity

2024/08/13 by Wang, Lidan · 1 citation
#35J20 #35J60 #35R02 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.06566

Abstract

In this paper, we study the following Kirchhoff-Choquard equation -(a+b ∫_ℤ³|∇ u|² d μ) Δu+h(x) u=(R_α∗|u|^p)|u|^p-2u, x∈ ℤ³, where a, b>0, α∈(0,3) are constants and R_α is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on potential function h, for p>2, we first establish the existence of ground state solutions based on the Nehari manifold. Subsequently, for p>4, we obtain the existence of ground state sign-changing solutions by adopting constrained minimization arguments on the sign-changing Nehari manifold.

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

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