Ground and Bound States of Nonlinear Schrödinger Equation

本文我們探討一個非線性薛丁格方程式。利用變分法上的技巧，我們分析能量泛函的幾何結構，找到了一個局部極小值以及一個鞍點。也因此我們證明了方程式存在兩個解，分別對應了基態以及束縛態。In this paper we consider a nonlinear Schrödinger equation. By Nehari manifold approach, the geometry of energy functional admits a minimum and a saddle point. Hence we can find two solutions of the equation which correspond to a ground state and a bound state.Contents Abstract v 1 Introduction and Main Results 1 2 Preliminary 3 3 Study on Nehari Manifold 7 4 Existence of Ground State 13 5 Existence of Bound State 16 References 1