一类双调和椭圆方程组基态解的存在性

Existence of Ground State Solution for a Kind of Biharmonic Elliptic Systems

运用Nehari流形的方法和集中紧性引理,研究了一类具有多重临界指数和Hardy项的双调和椭圆方程组,证明了在一定假设条件下,Hardy项系数分别为常系数和变系数时方程组正基态解的存在性,这些结果改进和推广了一些已知的结果.

In this paper,a class of biharmonic elliptic systems with multiple critical exponents and Hardy potential are studied.By virtue of the method of Nehari manifold and concentration compactness lemma.Under appropriate assumptions,the existence of positive ground state solution is proved,where the coefficient of Hardy-type terms are constants and functions respectively.Our main results improve and generalize some of the known results.