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

Vieri Benci, Carlo R. Grisanti, Anna Maria Micheletti

DOI: http://dx.doi.org/10.12775/TMNA.2005.031

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

Keywords


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

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