一类分数阶薛定谔方程的驻波解  

STANDING WAVE SOLUTIONS FOR FRACTIONAL SCHR DINGER EQUATIONS

作　　者：路慧芹 张悦 Lu Huiqin;Zhang Yue(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《山东师范大学学报（自然科学版）》2021年第2期144-147,共4页Journal of Shandong Normal University(Natural Science)

基　　金：山东省自然科学基金资助项目(ZR2018MA022).

摘　　要：分数阶薛定谔方程是分数阶量子力学中最基本的数学模型,它不仅可以描述不同物理背景下的非线性波的传输,而且也可以描述锥形光束的衍射、混沌和湍流等复杂现象,因而受到许多学者的广泛关注.Cheng M在文献[1]中通过Nehari流形方法研究了一类分数阶薛定谔方程,证明了当频率很小时方程驻波解的存在性.本文利用变分方法和环绕定理研究了该类分数阶薛定谔方程,得到了该类方程在非共振情况下非平凡驻波解的存在性,从而补充和推广了文献[1]的主要结果.Fractional Schrdinger equations are the most basic mathematical models in the fractional quantum mechanics.They can not only describe the propagation of nonlinear waves in different physical backgrounds,but also describe the diffraction of tapered beams,chaos and turbulence.Therefore,they have been widely concerned by many scholars.In[1],Cheng M had studied a class of fractional Schrdinger equations by Nehari manifold method,and had obtained the existence of standing wave solutions when the frequency is small.By using variational method and linking theorem,the existence of non-trivial standing wave solutions for the fractional Schr9 dinger equations is obtained in this paper.This work extends the related results obtained by Cheng M.

关 键 词：分数阶薛定谔方程 环绕定理 驻波解 

分 类 号：O175.25[理学—数学]