数学物理学报 ›› 2017, Vol. 37 ›› Issue (6): 1105-1118.

• 论文 • 上一篇    下一篇

一类带有不同Rellich项的临界双调和方程组的非平凡解

康东升, 熊萍   

  1. 中南民族大学数学与统计学学院 武汉 430074
  • 收稿日期:2016-04-12 修回日期:2017-04-22 出版日期:2017-12-26 发布日期:2017-12-26
  • 作者简介:康东升,E-mail:dongshengkang@scuec.edu.cn
  • 基金资助:
    中南民族大学中央高校基本科研业务费资金(CZP17015)

Biharmonic Systems Involving Critical Nonlinearities and Different Rellich-Type Potentials

Kang Dongsheng, Xiong Ping   

  1. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074
  • Received:2016-04-12 Revised:2017-04-22 Online:2017-12-26 Published:2017-12-26
  • Supported by:
    Supported by the Fundamental Research Funds for the Central Universities, South-Central University for Nationalities (CZP17015)

摘要: 该文研究一类带有多重临界Sobolev指数和不同Rellich位势项的双调和方程组.利用变分法得到在一定条件下相关最佳常数的达到函数对的存在形式和基本性质,并证明双调和方程组非平凡解的存在性.

关键词: 双调和方程组, 解, 临界Sobolev指数, Rellich位势项, 变分法

Abstract: In this paper, a system of biharmonic equations is investigated, which involves multiple critical Sobolev nonlinearities and different Rellich-type terms. The minimizers of the related best Soblev constant are found under certain assumptions and the existence of solutions to the system is established by variational arguments.

Key words: Biharmonic system, Solution, Critical exponent, Rellich potential, Variational method

中图分类号: 

  • O175.25