康东升,李 静,徐良顺.一类带有多重 Hardy 项和多重强耦合Hardy-Sobolev 临界项的椭圆方程组的正解[J].中南民族大学学报自然科学版,2017,(3):137-141
一类带有多重 Hardy 项和多重强耦合Hardy-Sobolev 临界项的椭圆方程组的正解
Positive Solutions to an Elliptic System Involving Multiple Hardy-TypeTerms and Multiple Strongly-Coupled Critical Hardy-Sobolev Terms
  
DOI:
中文关键词: 多重 Hardy 项  强耦合 Hardy-Sobolev 临界项  集中紧性原理  山路定理
英文关键词: multiple Hardy-type terms  strongly-coupled critical Hardy-Sobolev term  concentration compactness principle  Mountain Pass theorem
基金项目:国家自然科学基金资助项目(11601530);中南民族大学研究生科研创新项目(2017sycxjj083)
作者单位
康东升,李 静,徐良顺 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:
      研究了一类带有多重 Hardy 项和多重强耦合 Hardy-Sobolev 临界项的椭圆方程组, 运用集中紧性原理和山路定理,控制 Hardy 项系数和强耦合临界项指数, 证明了在一定条件下方程组正解的存在性, 首次把带有多重Hardy 项的临界椭圆方程的相关方法应用到带有多重 Hardy 项和强耦合 Hardy-Sobolev 临界项的椭圆方程组.
英文摘要:
      In this paper, an elliptic system is investigated, which involves multiple Hardy-type terms and strongly-coupled critical Hardy-Sobolev terms. By the concentration compactness principle and the Mountain Pass Theorem and by controlling the coefficients of Hardy-type terms and the exponents of strongly-coupled critical terms, the existence of positive solutions to the system is verified under certain conditions, and for the first time, the related methods for the critical elliptic equation involving multiple Hardy-type terms are extended to the system of critical elliptic equations involving multiple Hardy-type terms and strongly-coupled Hardy-Sobolev critical terms.
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