带陡峭位势的分数阶Schrodinger-Poisson系统的基态变号解  

Ground State Sign-changing Solution for Fractional Schrodinger-Poisson System with Steep Potential Well

作　　者：黄小庆 廖家锋 HUANG Xiao-qing;LIAO Jia-feng(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2024年第5期488-494,共7页Journal of China West Normal University(Natural Sciences)

基　　金：四川省自然科学基金项目(2023NSFSC0073)。

摘　　要：本文研究了带陡峭位势的分数阶Schrodinger-Poisson系统的基态变号解的存在性,由于系统中的位势是陡峭位势,这使得系统的能量泛函紧性缺失。运用约束变分法将能量泛函限制在约束集M_(λ)中,证明能量泛函的下确界可以达到,采用形变引理,得到了系统有1个基态变号解,基态变号解有2个结点域,并且基态变号解的能量严格大于基态解能量的2倍。This paper studies the existence of ground state sign-changing solution for a fractional Schrodinger-Poisson system with steep potential well.A lack of energy functional tightness is caused by the steep potential well in the system.The constraint variational method is employed to limit the energy functional to the constraint concentration M_(λ),which proves that the lower boundary of the energy functional can be reached.With the aid of the deformation lemma,it is found that the system has a ground state sign-changing solution which has two nodal domains,and the energy of the ground state sign-changing solution is strictly more than twice the energy of the ground state solution.

关 键 词：分数阶Schrodinger-Poisson系统 约束变分法 基态变号解 陡峭位势 

分 类 号：O177.91[理学—数学]