Abstract
In this paper we study the following nonlinear Schrödinger equations in $\mathbb{R}^N$:
$$
-\Delta u + V(x)u= g(u),\quad u \in H^1(\mathbb{R}^N),
$$
where $N \ge 2$, $V \in C^1(\mathbb{R}^N,\mathbb{R})$ and
$g \in C(\mathbb{R},\mathbb{R}).$ For a wide class of nonlinearities, which satisfy
the Berestycki-Lions type condition, we show the existence and multiplicity
of radially symmetric solutions. We use a new deformation argument under
a new version of the Palais-Smale condition.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University