Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
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DOI：
10.1112/jlms/jdu054
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发表时间：
2012-09
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影响因子：
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通讯作者：
Jianjun Zhang;Zhijie Chen;W. Zou
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文献类型：
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作者：
Jianjun Zhang;Zhijie Chen;W. Zou
本文研究了如下奇摄动椭圆型问题$$\开始{array}{ll}-ε 2\Delta u+V（x）u=f（u），\quad u \in H^1（R}^2），\end{array}$$-ε2Δu+V（x）u=f（u），u∈H1（R 2），其中f（s）具有Trudinger-Moser型临界增长.本文在f（s）上构造了一个在一定条件下集中于V的正局部极小点的孤立分量的局部束缚态解为ε→0.我们的结果完成了Byeon等人（Commun Partial Differ Equ 33：1113-1136，2008）对二维情况的分析，在这个意义上，在该论文中只考虑了亚临界生长。
AbstractIn this paper, we deal with the following singularly perturbed elliptic problem $$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}$$-ε2Δu+V(x)u=f(u),u∈H1(R2),where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as $${\varepsilon \rightarrow 0}$$ε→0 under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.