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X. P. Zhu, D. M. Cao. The concentration-compactness principle in nonlinear elliptic equations. Acta Mathematica Scientia, 1989, 9(3): 307-323.

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• 标题: 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

  作者: 朱红波

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

  期刊名称: 《Pure Mathematics》, Vol.2 No.2, 2012-04-26

  摘要: 本文考虑如下形式的非线性Schrödinger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 Schrödinger 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 .