引用本文:张黔, 邓志颖.含临界指数项和双重奇异项的Kirchhoff型椭圆边值方程的正解[J].西南师范大学学报(自然科学版),2020,45(2):11~19
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含临界指数项和双重奇异项的Kirchhoff型椭圆边值方程的正解
张黔, 邓志颖1,2
1. 重庆邮电大学 理学院 应用数学系, 重庆 400065;2. 重庆数联铭信科技有限公司, 重庆 401121
摘要:
讨论了一类含临界指数项和双重奇异项的Kirchhoff型椭圆边值方程.应用Lions集中紧性原理和Ekeland变分原理,证明了该方程在适当条件下正解的存在性与多重性,推广和改进了一些最近的结果.
关键词:  Kirchhoff型方程  Sobolev临界指数  奇异项  集中紧性原理  正解
DOI:10.13718/j.cnki.xsxb.2020.02.003
分类号:O175.25
基金项目:国家自然科学基金项目(11471235,11601052,11971339);重庆市基础与前沿研究计划重点项目(cstcjcyjBX0037).
Positive Solutions for Kirchhoff-Type Elliptic Boundary Value Equations with Critical Exponent and Double Singular Terms
ZHANG Qian, DENG Zhi-ying1,2
1. Department of Applied Mathematics, School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;2. Chongqing Shulian Mingxin Technology Limited Company, Chongqing 401121, China
Abstract:
This paper deals with a class of Kirchhoff-type elliptic boundary value equations involving critical exponent and double singular terms.Based upon the Lions concentration compactness principle and the Ekeland variational principle,we obtain the existence and multiplicity of positive solutions for the problem under the appropriate conditions,some recent results are generalized and significantly improved.
Key words:  Kirchhoff-type equation  Sobolev critical exponent  singular terms  the concentration compactness principle  positive solution
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