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A nonexistence result for a class of quasilinear Schrödinger equations with Berestycki-Lions conditions
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A nonexistence result for a class of quasilinear Schrödinger equations with Berestycki-Lions conditions
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Journal Article
A nonexistence result for a class of quasilinear Schrödinger equations with Berestycki-Lions conditions
2023
Overview
In this paper, we study the following quasilinear Schrödinger equation
−
Δ
u
+
V
(
x
)
u
−
[
Δ
(
1
+
u
2
)
1
/
2
]
u
2
(
1
+
u
2
)
1
/
2
=
h
(
u
)
,
x
∈
ℝ
N
, where
N
≥
3
,
2
*
=
2
N
N
−
2
, V(x) is a potential function. Unlike V ∈ C²(ℝ
N
), we only need to assume that V ∈ C¹(ℝ
N
). By using a change of variable, we prove the non-existence of ground state solutions with Berestycki-Lions conditions, which contain the superliner case:
lim
s
→
+
∞
h
(
s
)
s
=
+
∞
and asymptotically linear case:
lim
s
→
+
∞
h
(
s
)
s
=
η
. Our results extend and complement the results in related literature.
Publisher
University of Nis, Faculty of Sciences and Mathematics
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