康东升,刘梦茹,高蒙.带有多重强耦合Hardy项的临界椭圆方程组的基态解[J].中南民族大学学报自然科学版,2019,38(1):156-160
带有多重强耦合Hardy项的临界椭圆方程组的基态解
Ground state solutions to critical elliptic system with multiple strongly-coupled Hardy terms
  
DOI:10.12130/znmdzk.20190127
中文关键词: 强耦合Hardy项  临界指标  椭圆方程组  基态解
英文关键词: strongly-coupled Hardy term  critical exponent  elliptic system  ground state solution
基金项目:国家自然科学基金资助项目(11601530)
作者单位
康东升,刘梦茹,高蒙 中南民族大学 数学与统计学学院,武汉 430074 
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中文摘要:
      在全空间中研究了一类带有多重强耦合Hardy项的临界椭圆方程组,运用集中紧性原理和Schwartz对称化方法研究了极小化序列的收敛性,从而进一步证明了椭圆方程组基态解以及最佳Sobolev常数达到函数对的存在性.首次研究了此类椭圆方程组并证明了它的重要性质,为后续研究打下基础.
英文摘要:
      In this paper, a kind of critical elliptic system is studied in the whole space, which involves multiple strongly-coupled Hardy terms. By the concentration compactness principle and the Schwartz symmetrization methods, the convergence of minimizing sequence is proved. Furthermore, the existence of a ground state solution to the system and the extremal functions to the best Sobolev constant is proved. For the first time, this kind of elliptic system is studied and its important properties are proved, providing fundamental base for the further research.
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