Uniqueness of Positive Solutions to Scalar Field Equations with Harmonic Potential
Uniqueness of Positive Solutions to Scalar Field Equations with Harmonic Potential
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DOI：
10.1619/fesi.50.67
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Munemitsu Hirose;Masahito Ohta
中科院分区：
文献类型：
--
作者：
Munemitsu Hirose;Masahito Ohta
我们的目的是证明一类具有调和位势的非线性椭圆型方程在一定能量空间中正解的唯一性。这个问题是在研究一类非线性薛定谔方程的驻波稳定性时出现的，文[3]中用标准变分方法证明了椭圆型方程正解的存在性。此外，在文[5]中，我们还得到了n≥3下的唯一性，其中n表示空间的维度。本文给出了n=1和n=2的唯一性的证明。
Our purpose is to show the uniqueness of positive solutions for a nonlinear elliptic equation with a harmonic potential in some energy space. This problem arises in the study on the stability of standing waves for a nonlinear Schrodinger equation, and in [3], the existence of positive solutions to the ellipitc equation has been shown by the standard variational method. Moreover, in [5] we have derived the uniqueness under n ≥ 3, where n denotes the space dimension. In this paper, we give the proof of the uniqueness for n = 1 and n = 2.