Abstract
Abstract
In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension d of the following forms,
i
∂
t
u
+
∑
j
=
1
d
∂
x
j
4
u
=
V
t
,
x
u
,
and
i
∂
t
u
+
∑
j
=
1
d
∂
x
j
4
u
+
F
u
,
u
‾
=
0.
We show that a linear solution u with fast enough decay in certain Sobolev spaces at two different times has to be trivial. Consequently, if the difference between two nonlinear solutions u
1 and u
2 decays sufficiently fast at two different times, it implies that
u
1
≡
u
2
.
Funder
Undergraduate Research Opportunities Program at MIT
AMS-Simons travel grant
Cited by
1 articles.
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