Affiliation:
1. School of Mathematics and Physics , University of Science and Technology Beijing , Xueyuan Road 30, Haidian , Beijing 100083 , P. R. China
Abstract
Abstract
We consider ground states of the nonlinear fractional Schrödinger equation with potentials
(
-
Δ
)
s
u
+
V
(
x
)
u
=
f
(
x
,
u
)
,
s
∈
(
0
,
1
)
,
(-\Delta)^{s}u+V(x)u=f(x,u),\quad s\in(0,1),
on the whole space
ℝ
N
{\mathbb{R}^{N}}
, where V is a periodic non-negative nontrivial function on
ℝ
N
{\mathbb{R}^{N}}
and the nonlinear term f has some proper growth on u. Under uniform bounded assumptions about V, we can show the existence of a ground state. We extend the result of Li, Wang, and Zeng to the fractional case.
Subject
General Mathematics,Statistical and Nonlinear Physics
Cited by
1 articles.
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