摘要
非线性Schr9dinger耦合系统已成为研究热点,该类系统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。基于Ekeland变分原理和一些分析技巧,研究了一类带临界指数的非线性Schr9dinger耦合系统正基态解的存在性,对定义在无界域上与含有临界指数的耦合问题是其中比较困难的部分。首先,建立变分框架与定义Nehari流形和最低能量值,将求该类系统的解转化为求对应能量泛函的临界点。然后,当系统满足一定条件时,验证能量泛函满足山路几何结构,并估计能量值的取值范围。最后,利用集中紧性原理分两种情形得到该类系统非平凡基态解的存在性,同时获得的基态解可以是正基态解,推广了已有的研究结果。
The nonlinear Schr9 dinger coupled systems have become a research hotspot,this type of system is widely used in the fields of quantum mechanics,nonlinear optics,etc.in mathematical physics problems.Based on the Ekeland’s variational principle and some analytical techniques,the existence of a positive ground state solution of a class of nonlinear Schr9 dinger coupled systems with critical exponents is studied,the problem of coupled between defining unbounded domains and containing critical exponents is the more difficult part.Firstly,establish a variational framework and definition Nehari manifold and a lowest energy value,transforming the solution of this type of system into the critical point of the corresponding energy functional.Then,when the system meets certain conditions,it can be verified that the energy functional satisfies the mountain geometry,and estimate the range of the energy value.Finally,use the concentration-compactness principle to obtain the existence of the non-trivial ground state solution of this type of system in two situations,and the ground state solution obtained at the same time can be the positive ground state solution,which promotes the existing research results.
作者
贺书文
HE Shuwen(School of Science and Technology,Sichuan Minzu College,Kangding 626001,China)
出处
《四川轻化工大学学报（自然科学版）》
CAS
2021年第3期94-100,共7页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金项目(11461058)
四川民族学院科研项目(XYZB2010ZB)。
