Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs

2021/08/02 by Bobo Hua, Hua, Bobo, Wendi Xu +1 · 9 citations
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.00711

Abstract

In this paper, we study the nonlinear Schrödinger equation -Δu+V(x)u=f(x,u) on the lattice graph 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 ℤ^N to quasi-transitive graphs.

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