数学物理学报 ›› 2016, Vol. 36 ›› Issue (1): 65-79.

• 论文 • 上一篇    下一篇

分数阶耦合非线性Schrödinger方程组的山路解

魏公明, 李青   

  1. 上海理工大学理学院 上海 200093
  • 收稿日期:2015-08-03 修回日期:2015-12-23 出版日期:2016-02-25 发布日期:2016-02-25
  • 作者简介:魏公明,gmweixy@163.com;李青,qinglismile@163.com
  • 基金资助:

    国家自然科学基金(11471215)和沪江基金(B14005)资助

Mountain Pass Solutions for Fractional Coupled Nonlinear Schrödinger Systems

Wei Gongming, Li qing   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2015-08-03 Revised:2015-12-23 Online:2016-02-25 Published:2016-02-25
  • Supported by:

    Supported by the NSFC (11471215) and Hujiang Foundation of China (B14005)

摘要:

该文研究一类非线性分数阶Schrödinger方程组Dirichlet问题非平凡解的存在性.所用主要工具是分数阶Sobolev空间上的山路引理.要点是证明PS条件及该方程组的山路解是非平凡的.

关键词: 分数阶拉普拉斯算子, 临界点, 山路引理, PS条件, 极小能量解

Abstract:

In this paper, we study the existence of nontrivial solutions for fractional coupled nonlinear Schrödinger systems with Dirichlet boundary conditions. Our method is to use Mountain Pass Theorem in fractional order Sobolev spaces. The main points are to prove that the PS condition is satisfied and the mountain pass solution for the system is actually nontrivial.

Key words: Fractional Laplace operator, Critical point, Mountain Pass Theorem, Palais-Smale condition, Least energy solution

中图分类号: 

  • O175.2