数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (2): 443-470.doi: 10.1016/S0252-9602(13)60011-9

• 论文 • 上一篇    下一篇

POSITIVE SOLUTIONS FOR CRITICAL QUASILINEAR ELLIPTIC EQUATIONS WITH MIXED DIRICHLET-NEUMANN BOUNDARY CONDITIONS

丁凌|唐春雷*   

  1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;School of Mathematics and Computer Science, Hubei University of Arts and Science, Hubei 441053, China;Institute of Applied Physics and Computational Mathematics of Beijing, Beijing 100088, China; School of Mathematics and Statistics, Southwest University, Chongqing 400715, China  
  • 收稿日期:2011-11-22 修回日期:2012-05-12 出版日期:2013-03-20 发布日期:2013-03-20
  • 通讯作者: 唐春雷,tangcl@swu.edu.cn E-mail:xfdingling115111@sina.com;tangcl@swu.edu.cn
  • 基金资助:

    Supported by National Natural Science Foundation of China (11071198; 11101347), Postdoctor Foundation of China (2012M510363), and the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605; D20122501).

POSITIVE SOLUTIONS FOR CRITICAL QUASILINEAR ELLIPTIC EQUATIONS WITH MIXED DIRICHLET-NEUMANN BOUNDARY CONDITIONS

 DING Ling, TANG Chun-Lei*   

  1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;School of Mathematics and Computer Science, Hubei University of Arts and Science, Hubei 441053, China;Institute of Applied Physics and Computational Mathematics of Beijing, Beijing 100088, China; School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
  • Received:2011-11-22 Revised:2012-05-12 Online:2013-03-20 Published:2013-03-20
  • Contact: TANG Chun-Lei,tangcl@swu.edu.cn E-mail:xfdingling115111@sina.com;tangcl@swu.edu.cn
  • Supported by:

    Supported by National Natural Science Foundation of China (11071198; 11101347), Postdoctor Foundation of China (2012M510363), and the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605; D20122501).

摘要:

The existence and multiplicity of positive solutions are studied for a class of quasi-linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.

关键词: Mixed Dirichlet-Neumann boundary, quasilinear elliptic equations, Sobolev critical exponents, Ekeland’s variational principle, Mountain Pass Lemma

Abstract:

The existence and multiplicity of positive solutions are studied for a class of quasi-linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.

Key words: Mixed Dirichlet-Neumann boundary, quasilinear elliptic equations, Sobolev critical exponents, Ekeland’s variational principle, Mountain Pass Lemma

中图分类号: 

  • 35B33