论文标题
在晶格图上具有硬度重量的非线性Schrödinger方程的基态解决方案
The ground state solutions of nonlinear Schrödinger equations with Hardy weights on lattice graphs
论文作者
论文摘要
在本文中，我们研究了非线性schrödinger方程$$-ΔU+（v（x） - \fracρ{（| x |^2+1）}）操作员$-δ+V $。根据一些关于非线性$ f $的假设，我们证明了基态解决方案的存在和渐近行为，该解决方案具有较小的$ρ\ geq 0 $，由广义链接定理。
In this paper, we study the nonlinear Schrödinger equation $$ -Δu+(V(x)- \fracρ{(|x|^2+1)})u=f(x,u) $$ on the lattice graph $\mathbb{Z}^N$ with $N\geq 3$, where $V$ is a bounded periodic potential and $0$ lies in a spectral gap of the Schrödinger operator $-Δ+V$. Under some assumptions on the nonlinearity $f$, we prove the existence and asymptotic behavior of ground state solutions with small $ρ\geq 0$ by the generalized linking theorem.
