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带有非自治项的非线性Schrödinger方程的基态解的存在性
Ground States of Nonlinear Schrödinger Equation with Non-Autonomous Nonlinearity

DOI: 10.12677/pm.2012.22011, PP. 62-72

Keywords: 非线性Schrödinger方程;基态解;集中紧致原理
Nonlinear Schrödinger Equation
, Ground State Solutions, Concentration Compactness

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Abstract:

本文考虑如下形式的非线性Schr?dinger方程 (P)。利用有界区域逼近和集中紧致原理,当位势函数不恒等于常数,非线性项 不恒等于 ,本文证明了方程(P)存在最低能量解。
In this paper, we are concerned with the following nonlinear Schr?dinger equation
(P). By using the bounded domain approximate scheme and concen-tration compactness principle, we prove the existence of a ground state solution of (P) on the Nehari manifold when constant and .

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