Semiclassical ground state solutions for a Schrödinger equation in R2 with critical exponential growth
Semiclassical ground state solutions for a Schrödinger equation in R2 with critical exponential growth
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DOI：
10.1002/mana.201400267
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发表时间：
2016-04
影响因子：
1
通讯作者：
B. Tao;Zhibin Liu;Minbo Yang
中科院分区：
文献类型：
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作者：
B. Tao;Zhibin Liu;Minbo Yang
考虑一个薛定谔方程− ε 2Δu+V（x）u=Q（x）f（u）in R 2，其中V（x）和Q（x）是R 2上的两个连续真实的函数，ε是一个正参数，非线性系数f在Trudinger-Moser不等式意义下是临界指数增长的.通过截断位势V（x）和Q（x），我们用变分方法建立了R2中临界薛定谔方程的一些新的存在性和集中性结果.作为一种特殊情况，我们观察到浓度出现在非线性势Q（x）的最大值处，这补充了，。
Consider a Schrödinger equation −ɛ2Δu+V(x)u=Q(x)f(u)inR2,where V(x) and Q(x) are two continuous real functions on R2 , ε is a positive parameter, the nonlinearity f is assumed to be of critical exponential growth in the sense of the Trudinger‐Moser inequality. By truncating the potentials V(x) and Q(x) , we are able to establish some new existence and concentration results for critical Schrödinger equation in R2 by variational methods. As a particular case, we observe that the concentration appears at the maximum set of the nonlinear potential Q(x) which complements the results in , .