Positive solutions for Schrödinger system with asymptotically periodic potentials

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• 作者：Jun Wang^a ; ^{wangmath2011@126.com" class="auth_mail" title="E-mail the corresponding author} ; Qing He^a ; ^{18252586526@126.com" class="auth_mail" title="E-mail the corresponding author} ; Lu Xiao^b ; ^{hnlulu@126.com" class="auth_mail" title="E-mail the corresponding author} ; Fubao Zhang^c ; ^{zhangfubao@seu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Weakly coupled Schrö ; dinger system ; Positive solutions ; Variational methods
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：134
• 期：Complete
• 页码：215-235
• 全文大小：686 K

文摘

This paper is concerned with the following class of elliptic equations where d05f9" title="Click to view the MathML source">u,v∈H¹(R^N)$u,v\in H^1\left({\mathbb{R}}^N\right)$, N≤3$N\le 3$, μ,ν,β>0$\mu ,\nu ,\beta >0$ are coupling constants, λ(x)$\lambda \left(x\right)$ and κ(x)$\kappa \left(x\right)$ are asymptotically periodic functions, f$f$ and 20db8d2a58e9b9" title="Click to view the MathML source">g$g$ are continuous functions with subcritical growth. This type of system arises, in particular, in models in Bose–Einstein condensates theory. We prove the existence of positive solution for this weakly coupled system with β>0$\beta >0$ sufficiently large. Furthermore, we obtain some sufficient conditions for the nonexistence of positive solutions.