康东升,刘晓楠,曹玉平.带有Rellich项的临界双调和方程组的研究[J].中南民族大学学报自然科学版,2018,(1):149-153
带有Rellich项的临界双调和方程组的研究
On the Critical Biharmonic Equations Involving the Rellich-Type Terms
  
DOI:
中文关键词: 双调和  临界  方程组  非平凡解
英文关键词: biharmonic  critical  equations  nontrivial solution
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基金资助项目(2018sycxjj111)
作者单位
康东升1,刘晓楠1,曹玉平2 1 中南民族大学 数学与统计学学院武汉 430074
2 中南民族大学 图书馆武汉 430074 
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中文摘要:
      在全空间中研究了一类带有Rellich 项的临界双调和方程组, 得到了方程组的基态解.在有界区域上研究了另一类带有Rellich 项和线性扰动项的临界双调和方程组, 运用变分法证明了方程组在一定条件下存在非平凡解,首次把单个奇异双调和方程的相关结果推广到对应的方程组.
英文摘要:
      In this paper, a class of critical biharmonic equations involving the Rellich-type terms were investigated in RN and the ground state solutions are obtained. Another class of critical biharmonic equations was investigated in a bounded domain, which involves the Rellich-type terms and linear perturbations. By variational arguments, the existence of nontrivial solutions to the problem was established under certain conditions, and for the first time, the related conclusions for the single singular biharmonic equation were extended to the system of corresponding equations.
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