﻿ 广义拟线性Schrödinger方程的径向解 Radial Solutions for Generalized Quasilinear Schrödinger Equations

Pure Mathematics
Vol.07 No.03(2017), Article ID:20515,6 pages
10.12677/PM.2017.73018

Radial Solutions for Generalized Quasilinear Schrödinger Equations

Qing Li, Yangxin Yao*

Department of Mathematics, South China University of Technology, Guangzhou Guangdong

Received: Apr. 27th, 2017; accepted: May 12th, 2017; published: May 16th, 2017

ABSTRACT

By using the ODE method, we study the existence result of radial solutions for generalized quasilinear Schrödinger equations arising from mathematical physics.

Keywords:Schrödinger Equations, Radial Solutions, Contraction Mappings, Continuation Theorem

Copyright © 2017 by authors and Hans Publishers Inc.

1. 引言

(1.1)

(1.2)

。把代入方程(1.2)后消去含t的项，便得到方程(1.1)。

2. 定理的证明

，根据的条件，反函数存在。

(2.1)

(2.2)

(2.3)

(2.4)

(2.5)

(2.6)

(2.7)

(2.8)

(2.9)

(2.10)

(1)是整体解；

(2) 存在一点，使得：

(2.11)

(2.12)

(2.13)

(2.14)

(2.15)

。如果公式(2.12)成立，由的有下界性可以得出的有界性。

Radial Solutions for Generalized Quasilinear Schrödinger Equations[J]. 理论数学, 2017, 07(03): 149-154. http://dx.doi.org/10.12677/PM.2017.73018

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7. NOTES

*通讯作者。