{"title":"非径向势Chern-Simons-Schrödinger系统的多峰解","authors":"Jin Deng, W. Long, Jianfu Yang","doi":"10.57262/die036-0910-813","DOIUrl":null,"url":null,"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 $0<h<h_0$, problem \\eqref{eqabstr} has a nontrivial static solution $(\\Psi_h, A_0^h, A_1^h,A_2^h)$. Moreover, $\\Psi_h$ is a positive non-radial function with $k$ positive peaks, which approach to the local maximum point of $V(x)$ as $h\\to 0^+$.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Multi-Peak solutions to Chern-Simons-Schrödinger systems with non-radial potential\",\"authors\":\"Jin Deng, W. Long, Jianfu Yang\",\"doi\":\"10.57262/die036-0910-813\",\"DOIUrl\":null,\"url\":null,\"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 $0<h<h_0$, problem \\\\eqref{eqabstr} has a nontrivial static solution $(\\\\Psi_h, A_0^h, A_1^h,A_2^h)$. Moreover, $\\\\Psi_h$ is a positive non-radial function with $k$ positive peaks, which approach to the local maximum point of $V(x)$ as $h\\\\to 0^+$.\",\"PeriodicalId\":50581,\"journal\":{\"name\":\"Differential and Integral Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2020-07-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential and Integral Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/die036-0910-813\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential and Integral Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/die036-0910-813","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multi-Peak solutions to Chern-Simons-Schrödinger systems with non-radial potential
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
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.