| 摘要: |
| 非线性 Schrdinger 方程被广泛应用于数学物理问题中的量子力学、非线性光学等领域，其中非线性 Schrdinger 耦合系统已成为研究热点，对该系统优化和改进非线性项的条件和带周期函数问题是其中比较困难的部分，针对这种定义在无界区域上的耦合问题，提出了一类带多个不同周期函数的非线性 Schrdinger 耦合系统方程；基于变分法和一些分析技巧，将求该类系统的解转化为求对应能量泛函的临界点问题；当该类系统满足适当条件时，可以验证其能量泛函满足山路几何结构，得到一组有界非负的(Ce)c序列，再利用集中紧性原理分两种情形得到其非平凡非负解的存在性；最后由强极大值原理获得该类系统正解的存在性，推广了已有的研究结果。 |
| 关键词: Schrdinger耦合系统 变分法 非平凡正解 |
| DOI： |
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| Positive Solutions of a Class of Nonlinear Schrdinger Coupled Systems |
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HE Shu-wen,WEN Xiao-bo,YUAN Dong-lei1,2
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1.School of Science and Technology,Sichuan Minzu College,Sichuan Kangding 626001, China;2.School of Mathematics and Statistics, Southwest University, Chongqing 400715,China
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| Abstract: |
| The nonlinear Schrdinger equations are widely used in the fields of quantum mechanics, nonlinear optics, etc. in mathematical physics problems, the nonlinear Schrdinger coupled systems have become a research hotspot. The conditions for the optimization and improvement of the nonlinear terms and the periodic function problems are among more difficult parts, a class of nonlinear Schrdinger coupled system equations with multiple periodic functions is proposed for the coupling problem of this definition on unbounded regions.Based on variational method and some analytical techniques, the solutions of this kind of systems are transformed into the critical points problem of the corresponding energy functional; when the system satisfies the appropriate conditions, it can be verified that the energy functional satisfies the mountain geometry, and a set of bounded non negative (Ce)c sequences is obtained and reused. The compactness principle is used in two cases to obtain the existence of non trivial non negative solutions.Finally, the existence of positive solutions of such systems is obtained by the strong maximum principle,it promotes the existing research results. |
| Key words: Schrdinger coupled systems variational method non trivial positive solution |
