Author:
Chen Shaowei,Gou Tianxiang
Abstract
Abstract
In this paper, we are concerned with semiclassical states to the nonlinear Dirac equation with Sobolev critical exponent
−
i
ϵ
α
⋅
∇
u
+
a
β
u
+
V
(
x
)
u
=
|
u
|
q
−
2
u
+
|
u
|
u
in
R
3
, where
u
:
R
3
→
C
4
, 2 < q < 3, ϵ > 0 is a small parameter, a > 0 is a constant, α = (α
1, α
2, α
3), α
j
and β are 4 × 4 Pauli-Dirac matrices. We construct an infinite sequence of semiclassical states with higher energies concentrating around the local minimum points of the potential V. The problem is strongly indefinite and the solutions correspond to critical points of the underlying energy functional at energy levels where compactness condition breaks down. The proof relies on truncation techniques, blow-up arguments together with a local type Pohozaev identity.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献