Abstract
We consider the following nonlinear fractional Schrödinger equation:
$$ (-\triangle )^{s} u+V(x)u=g(u) \quad \text{in } \mathbb{R} ^{N}, $$
(
−
△
)
s
u
+
V
(
x
)
u
=
g
(
u
)
in
R
N
,
where $s\in (0, 1)$
s
∈
(
0
,
1
)
, $N>2s$
N
>
2
s
, $V(x)$
V
(
x
)
is differentiable, and $g\in C ^{1}(\mathbb{R} , \mathbb{R} )$
g
∈
C
1
(
R
,
R
)
. By exploiting the minimization method with a constraint over Pohoz̆aev manifold, we obtain the existence of ground state solutions. With the help of Pohoz̆aev identity we also process the existence of the least energy solutions for the above equation. Our results improve the existing study on this nonlocal problem with Berestycki–Lions type nonlinearity to the one that does not need the oddness assumption.
Existence of ground state solutions for a quasilinear Schrödinger equation with critical growth
