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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:

第22卷

期数:

2017年第2期

页码:

75-80

栏目:

数理科学与信息工程

出版日期:

2017-03-28

文章信息/Info

Title:

Positive and Negative Solutions of a Schrodinger Equation with Constraint in H1(RN)

作者:

刘竞坤1; 范琦2

(1.集美大学诚毅学院,福建 厦门 361021;2.厦门思泰克智能科技股份有限公司,福建 厦门 361100)

Author(s):

LIU Jingkun1; FAN Qi2

(1.Chengyi University College,Jimei University,Xiamen 361021,China;2.Xiamen Sinic-Tek Intelligent Technology Co.,Ltd,Xiamen 361100,China)

关键词:

Schrodinger方程; 正解; 负解; 周期; (PS)c序列; 拓扑度理论

Keywords:

Schrodinger equation; positive solution; negative solution; period; (PS)c-sequence; topology degree theory

分类号:

-

DOI:

-

文献标志码:

A

摘要:

应用变分方法，以拓扑度理论为依据，研究H1(RN)空间上一类带限制的半线性Schrodinger方程。通过构造适当的伪梯度向量场，解决带限制的半线性Schrodinger方程的Cauchy问题，证明其在周期和适当限制条件下解的存在性，并获得带限制的半线性椭圆特征问题的一个正解与一个负解。

Abstract:

Based on topology degree theory, variational method was applied to research a class of semilinear Schrodinger equation in H1(RN)with constraint in this paper. By constructing pseudo-gradient vector field, the Cauchy problem was solved and the existence of solution under the periodic and appropriate condition was proved. Finally, a positive solution and a negative solution of the semilinear elliptic problem with constraint were obtained.

参考文献/References:

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相似文献/References:

[1]陈应生,汪东树.z非线性四阶两点积分边值问题正解的存在性[J].集美大学学报(自然科学版),2012,17(5):379.
　CHEN Ying-shengWANG Dong-shu.Existence of Positive Solutions for Nonlinear Fourth-order Two-point Integral Boundary Value Problems[J].Journal of Jimei University,2012,17(2):379.
[2]周梦云,蓝永艺.一类拟线性薛定谔方程解的存在性[J].集美大学学报(自然科学版),2024,29(4):365.
　ZHOU Mengyun,LAN Yongyi.Existence of Solutions for a Class of Quasilinear Schrodinger Equation[J].Journal of Jimei University,2024,29(2):365.

备注/Memo

备注/Memo:

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更新日期/Last Update: 2017-05-19