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math.AP2024
Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity
Lidan Wang
In this paper, we study the following Kirchhoff-Choquard equation $$ -\left(a+b \int_{\mathbb{Z}^3}|\nabla u|^{2} d μ\right) Δu+h(x) u=\left(R_α\ast|u|^{p}\right)|u|^{p-2}u,\quad x…
math.AP2024
Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations
Lidan Wang
In this paper, we study the discrete logarithmic Kirchhoff equation $$ -\left(a+b \int_{\mathbb{Z}^3}|\nabla u|^{2} d μ\right) Δu+(λh(x)+1) u=|u|^{p-2}u \log u^{2}, \quad x\in \mat…
math.AP2023
Solutions to discrete fractional Schödinger equations
Lidan Wang
In this paper, we study the discrete fractional Schrödinger equation where and the nonlocal oper…
math.AP2022
The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth
Ruowei Li, Lidan Wang
In this paper, we study the nonlinear Choquard equation \begin{eqnarray*} Δ^{2}u-Δu+(1+λa(x))u=(R_α\ast|u|^{p})|u|^{p-2}u \end{eqnarray*} on a Cayley graph of a discrete group of p…