### Existence and non existence of the ground state solution for the nonlinear Schroedinger equations with $V(\infty)=0$

#### Abstract

We study the existence of the ground state

solution of the problem

$$

\cases

-\Delta u+V(x)u=f'(u) & x\in\mathbb R^N, \\

u(x)> 0,

\endcases

$$

under the assumption that

$\lim_{x\to\infty}V(x)=0$.

solution of the problem

$$

\cases

-\Delta u+V(x)u=f'(u) & x\in\mathbb R^N, \\

u(x)> 0,

\endcases

$$

under the assumption that

$\lim_{x\to\infty}V(x)=0$.

#### Keywords

Nonlinear Schroedinger equation; variational methods; ground state solution; Orlicz spaces

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