| Abstract: |
| In this talk, we consider the following NLS equations in $\mathbf{R}^N$:
$$-\Delta u + V(x)u= g(u),\ u \in H^1(\mathbf{R}^N),
$$
where $N \ge 2$, $V \in C^1(\mathbf{R}^N,\mathbf{R})$ and
$g \in C(\mathbf{R},\mathbf{R}).$ 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. |
|