Multi-Peak solutions to Chern-Simons-Schrödinger systems with non-radial potential

IF 1.8 4区 数学 Q1 MATHEMATICS
Jin Deng, W. Long, Jianfu Yang
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引用次数: 2

Abstract

In this paper, we consider the existence of static solutions to the nonlinear Chern-Simons-Schrodinger system \begin{equation}\label{eqabstr} \left\{\begin{array}{ll} -ihD_0\Psi-h^2(D_1D_1+D_2D_2)\Psi+V\Psi=|\Psi|^{p-2}\Psi,\\ \partial_0A_1-\partial_1A_0=-\frac 12ih[\overline{\Psi}D_2\Psi-\Psi\overline{D_2\Psi}],\\ \partial_0A_2-\partial_2A_0=\frac 12ih[\overline{\Psi}D_1\Psi-\Psi\overline{D_1\Psi}],\\ \partial_1A_2-\partial_2A_1=-\frac12|\Psi|^2,\\ \end{array} \right. \end{equation} where $p>2$ and non-radial potential $V(x)$ satisfies some certain conditions. We show that for every positive integer $k$, there exists $h_0>0$ such that for $0
非径向势Chern-Simons-Schrödinger系统的多峰解
本文考虑非线性chen - simons - schrodinger系统\begin{equation}\label{eqabstr} \left\{\begin{array}{ll} -ihD_0\Psi-h^2(D_1D_1+D_2D_2)\Psi+V\Psi=|\Psi|^{p-2}\Psi,\\ \partial_0A_1-\partial_1A_0=-\frac 12ih[\overline{\Psi}D_2\Psi-\Psi\overline{D_2\Psi}],\\ \partial_0A_2-\partial_2A_0=\frac 12ih[\overline{\Psi}D_1\Psi-\Psi\overline{D_1\Psi}],\\ \partial_1A_2-\partial_2A_1=-\frac12|\Psi|^2,\\ \end{array} \right. \end{equation}静态解的存在性,其中$p>2$和非径向势$V(x)$满足一定条件。我们证明,对于每一个正整数$k$,存在$h_0>0$,使得对于$0
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来源期刊
Differential and Integral Equations
Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.40
自引率
0.00%
发文量
0
审稿时长
6-12 weeks
期刊介绍: Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.
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