北京航空航天大学学报 ›› 1999, Vol. 25 ›› Issue (2): 221-224.

• 论文 • 上一篇    下一篇

一类加权不等式及在临界指数问题中的应用

郭定辉   

  1. 北京航空航天大学 应用数理系
  • 收稿日期:1997-10-24 出版日期:1999-02-28 发布日期:2010-09-28
  • 作者简介:男 33岁 副教授 100083 北京
  • 基金资助:

    国家自然科学基金(19401004)资助项目

Some Weighted Inequalities on Polyharmonic Operators and Applications

Guo Dinghui   

  1. Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics
  • Received:1997-10-24 Online:1999-02-28 Published:2010-09-28

摘要: 研究了关于调和算子的加权不等式,推广了Bernis等人关于类似问题的结果,并且得到一些新结果.利用这些新结果,讨论了关于半线性部分是多调和算子的临界指数问题. 改进了问题存在非平凡径向解的必要条件,使该问题存在非平凡径向解的范围比已知的范围增大一倍.

Abstract: This work is devoted to weighted inequalities on polyharmonic operators and their applications to the critical exponent problems of semilinear polyharmonic operator with Dirichlet boundary value conditions. Some newer weighted inequalities on polyharmonic operator are obtained. By applying these new weighted inequalities to the critical exponent problems, it obtains a preferable necessary condition for nontrivial radial solutions of the critical exponent problems of semilinear polyharmonic operator with Dirichlet boundary conditions existing. This preferable necessary condition extends the scope in which the critical exponent problems has nontrivial radial solutions to two times of that in Bernis' paper.

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