{"title":"Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system","authors":"Jianqing Chen, Qian Zhang","doi":"10.57262/die/1610420451","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the following quasilinear Schr\\\"{o}dinger system in the entire space $\\mathbb R^{N}$($N\\geq3$): $$\\left\\{\\begin{align}&-\\Delta u+A(x)u-\\frac{1}{2}\\triangle(u^{2})u = \\frac{2\\alpha}{\\alpha+\\beta}|u|^{\\alpha-2}u|v|^{\\beta},\\\\&-\\Delta v+Bv-\\frac{1}{2}\\triangle(v^{2})v=\\frac{2\\beta}{\\alpha+\\beta}|u|^{\\alpha}|v|^{\\beta-2}v.\\end{align}\\right. $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $\\alpha,\\beta>1$, $2<\\alpha+\\beta<\\frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schr\\\"{o}dinger systems, J. Math. Anal. Appl. 389 (2012) 322).","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-01-01","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/die/1610420451","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
This paper is concerned with the following quasilinear Schr\"{o}dinger system in the entire space $\mathbb R^{N}$($N\geq3$): $$\left\{\begin{align}&-\Delta u+A(x)u-\frac{1}{2}\triangle(u^{2})u = \frac{2\alpha}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\&-\Delta v+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v.\end{align}\right. $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $\alpha,\beta>1$, $2<\alpha+\beta<\frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schr\"{o}dinger systems, J. Math. Anal. Appl. 389 (2012) 322).
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.