Least energy sign-changing solutions for nonlinear Schrödinger equations with indefinite-sign and vanishing potential

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• 作者：Hongliang Liu ^{math_lhliang@163.com" class="auth_mail" title="E-mail the corresponding author} ; Haibo Chen ; ^{math_chb@csu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xiaoxia Yang
• 关键词：Schrö ; dinger equations ; Sign-changing solutions ; Indefinite-sign and vanishing potential
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：53
• 期：Complete
• 页码：100-106
• 全文大小：621 K

文摘

We consider the following nonlinear stationary Schrödinger equation where N&ge;3$N\&<font\; color="red">ge</font>;3$, λ>0$\lambda >0$ and V(x)$V\left(x\right)$ changes sign and may vanish at infinity. Under some suitable conditions, the least energy solution is obtained by using variational methods. Moreover, the solution changes sign when λ$\lambda$ is sufficiently large. Our result unifies and improves the recent one in the literature.