Affiliation:
1. School of Science, Guangxi University of Science and Technology , Liuzhou , 545006 , P. R. China
2. College of Mathematics, Faculty of Science, Beijing University of Technology , Beijing , 100124 , P. R. China
Abstract
Abstract
The purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian
(
−
Δ
)
p
s
u
(
x
)
+
λ
V
(
x
)
u
(
x
)
p
−
1
=
u
(
x
)
q
−
1
,
u
(
x
)
≥
0
,
x
∈
R
N
,
{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x)u{\left(x)}^{p-1}=u{\left(x)}^{q-1},\hspace{1em}u\left(x)\ge 0,\hspace{0.33em}x\in {{\mathbb{R}}}^{N},
where
λ
>
0
\lambda \gt 0
is a parameter,
1
<
p
<
q
<
N
p
N
−
s
p
1\lt p\lt q\lt \frac{Np}{N-sp}
,
N
≥
2
N\ge 2
, and
V
(
x
)
V\left(x)
is a real continuous function on
R
N
{{\mathbb{R}}}^{N}
. For
λ
\lambda
large enough, the existence of ground state solutions are obtained, and they localize near the potential well int
(
V
−
1
(
0
)
)
\left({V}^{-1}\left(0))
.