Infinitely many radial and non-radial solutions for a fractional Schrödinger equation

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• 作者：Wen Zhang^a ; ^{zwmath2011@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xianhua Tang^a ; ^{tangxh@mail.csu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jian Zhang^b ; ^{zhangjian433130@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fractional Schrö ; dinger equations ; Radial solution ; Non-radial solution ; Variational methods
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：3
• 页码：737-747
• 全文大小：394 K

文摘

In this paper, we study the following fractional Schrödinger equation where (−Δ)^s(s∈(0,1))${(-\Delta )}^s(s\in (0,1))$ denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions for N≥2$N\ge 2$, a sequence of non-radial solutions for N=4$N=4$ or N≥6$N\ge 6$, and a non-radial solution for N=5$N=5$.