Abstract
We deal with a class on nonlinear Schrödinger equations (NLS) with potentials
V(x)\sim |x|^{-\alpha}
,
0
, and
K(x)\sim |x|^{-\beta}
,
\beta>0
. Working in weighted Sobolev spaces, the existence of ground states
v_{\varepsilon}
belonging to
W^{1,2}(\mathbb R^n)
is proved under the assumption that
\sigma
for some
\sigma=\sigma_{N,\alpha,\beta}
. Furthermore, it is shown that
v_{\varepsilon}
are
spikes
concentrating at a minimum of
{\mathcal A}=V^{\theta}K^{-2/(p-1)}
, where
\theta= (p+1)/(p-1)-1/2
.