临界和超临界的分数阶Schrödinger-Poisson系统正的径向基态解  

Positive radial ground state solutions to critical and supercritical fractional Schrödinger-Poisson systems

作　　者：沈真真 许勇强 SHEN Zhenzhen;XU Yongqiang(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《厦门大学学报（自然科学版）》2024年第6期1106-1111,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11571159);福建省自然科学基金(2017J01562);中国博士后科学基金(2016M592088)。

摘　　要：[目的]考虑一类带有临界和超临界指数的分数阶Schrödinger-Poisson系统正的径向基态解的存在性问题.[方法]先利用变分方法把该系统的解转化为对应的能量泛函的临界点,然后运用Nehari流形方法和山路定理找到系统的临界点.[结果]该系统在一定的条件下存在正的径向基态解.[结论]将一般的整数阶Schrödinger-Poisson系统解的存在性问题推广到分数阶情形,丰富和完善已有文献的结果.[Objective]The existence of positive radial ground state solutions for a class of fractional Schrödinger-Poisson systems with critical and supercritical exponents is considered.[Methods]First,the solution of the system is transformed into the critical point of the corresponding energy functional by using the variational method,and then the critical point of this system is found by using the Nehari manifold method and the mountain pass theorem.[Results]Finally,in the system,a positive radial ground state solution is obtained under certain conditions.[Conclusion]The existence of solutions for the general integer-order Schrödinger-Poisson system is extended to the fractional-order case.Hopefully,our proposed study may enrich and improve results of the existing literature.

关 键 词：分数阶Schrödinger-Poisson系统 临界指数 超临界指数 NEHARI流形 山路定理 

分 类 号：O175.25[理学—数学]