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

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 نشر من قبل Wendi Xu
 تاريخ النشر 2021
  مجال البحث فيزياء
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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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