Existence of ground state solutions to some Nonlinear Schr\"{o}dinger equations on lattice graphs

Bobo Hua; Wendi Xu

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arXiv · 2108.00711

Existence of ground state solutions to some Nonlinear Schr\"{o}dinger equations on lattice graphs

Bobo Hua·Wendi Xu

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Abstract

In this paper, we study the nonlinear Schr\"{o}dinger equation $ -\Delta u+V(x)u=f(x,u) $on the lattice graph $ \mathbb{Z}^{N}$. Using the Nehari method, we prove that when $f$ satisfies some growth conditions and the potential function $V$ is periodic or bounded, the above equation admits a ground state solution. Moreover, we extend our results from $\mathbb{Z}^{N}$ to quasi-transitive graphs.

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Bobo Hua, Wendi Xu. 2021-08-02. Existence of ground state solutions to some Nonlinear Schr\"{o}dinger equations on lattice graphs. https://arxiv.org/abs/2108.00711

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