Least energy solutions for a weakly coupled fractional Schrödinger system

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• 作者：Qing Guo ; ^{guoqing@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Xiaoming He ^{xmhe923@muc.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J20 ; 35J65
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：132
• 期：Complete
• 页码：141-159
• 全文大小：650 K

文摘

In this paper, we consider the following system of two weakly coupled fractional nonlinear Schrödinger equations By use of the s-harmonic extension technique, we establish the existence of a nontrivial least energy solution of the system via variational methods. Especially, in the autonomous case i.e. class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003752&_mathId=si2.gif&_user=111111111&_pii=S0362546X15003752&_rdoc=1&_issn=0362546X&md5=f403cd644fa2bde752c0d30f355dd419" title="Click to view the MathML source">b(x)≡bclass="mathContainer hidden">class="mathCode">$b\left(x\right)\equiv b$, a positive least energy solution with both nontrivial components is obtained.