Electron. J. Differential Equations,
Vol. 2017 (2017), No. 282, pp. 113.
Least energy signchanging solutions for the nonlinear
SchrodingerPoisson system
Chao Ji, Fei Fang, Binlin Zhang
Abstract:
This article concerns the existence of the least energy signchanging
solutions for the SchrodingerPoisson system
Because the socalled nonlocal term
is involved in the
system, the variational functional of the above system has totally different
properties from the case of
.
By constraint variational method
and quantitative deformation lemma, we prove that the above problem has one
least energy signchanging solution. Moreover, for any
,
we show that the energy of a signchanging solution is strictly larger than
twice of the ground state energy. Finally, we consider
as a
parameter and study the convergence property of the least energy signchanging
solutions as
.
Submitted September 9, 2017. Published November 13, 2017.
Math Subject Classifications: 35J20, 35J60.
Key Words: SchrodingerPoisson system; signchanging solutions;
constraint variational method; quantitative deformation lemma.
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Chao Ji
Department of Mathematics
East China University of Science and Technology
Shanghai 200237, China
email: jichao@ecust.edu.cn


Fei Fang
Department of Mathematics
Beijing Technology and Business University
Beijing 100048, China
email: fangfei68@163.com


Binlin Zhang
Department of Mathematics
Heilongjiang Institute of Technology
Harbin 150050, China
email: zhangbinlin2012@163.com

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