【摘要】 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.更多还原

【Abstract】 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.更多还原