带有Rellich项的临界双调和方程组的研究

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.%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.