带有耦合Rellich项的临界双调和方程组解的存在性

Existence of solutions to critical biharmonic systems involving coupled Rellich terms

研究了包含多重Rellich项和强耦合临界非线性项的两类临界双调和方程组,首先研究了相关最佳Sobolev常数的达到函数对;其次,在一定的假设条件,利用变分法的山路定理证明了非平凡解的存在性.本文中的双调和方程组是首次被研究,所得到的结果都是新的.

We study two kinds of critical biharmonic systems,which involve multiple Rellich-type terms and strongly-coupled critical nonlinearities.Firstly,we investigate the minimizers of extremal function to the related best Sobolev constant.Secondly,under certain assumptions,we prove the existence of the nontrivial solutions by the Mountain-Pass Theorem of variational methods.The biharmonic systems in this paper are studied for the first time and the conclusions obtained are all new.