Emden-Fowler方程奇异边值问题的无穷多高能量解  

Infinitely Many High Energy Solutions to Singular Emden-Fowler Equation

作　　者：赵月云 莫帅 张海燕 毛安民[1] ZHAO Yueyun;MO Shuai;ZHANG Haiyan;MAO Anmin(School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China)

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165

出　　处：《应用泛函分析学报》2020年第3期150-155,共6页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11471187)。

摘　　要：本文研究一类Emden-Fowler方程奇异边值问题{-ü+u=μ(x)|u|^q-2u+λ|u|^p-2u,x∈(0,1),u(0)=u(1)=0,其中μ(x)可以在无穷多个点存在奇异性.在满足经典的Ambrosetti-Rabinowitz条件下,本文利用喷泉定理证明了上述方程存在无穷多高能量解,所得结论是对已有相关结果的推广.In this paper we consider singular Emden-Fowler equation with Dirichlet boundary value condition.By using Fountain theorem method,we obtained the existence of infinitely many high energy solutions and our work improves and extends some existing works.

关 键 词：奇异边值问题 变分法 喷泉定理 

分 类 号：O175.8[理学—数学]