带有吸引Hardy项的临界椭圆方程组解的渐近同步

Asymptotic synchronization of solutions to critical elliptic systems involving attractive Hardy-type terms

研究了一个由2个椭圆方程组成的方程组,它带有p-Laplacian算子、耦合吸引的Hardy项和多个临界非线性项,证明了方程组的径向对称严格递减的解在原点和无穷远处的渐近性质.即使是在p=2时这些结果也是新的,首次发现解中的两个函数在原点和无穷远处是渐近同步的.

In this paper,a system of two elliptic equations is studied,which involves the p-Laplacian operator,coupled attractive Hardy terms and multiple critical nonlinearities.The asymptotic properties at the origin and at infinity of radially symmetric and strictly decreasing solutions are proved and the results are new even in the case of p=2.It is found for the first time that two components in the solutions are asymptotically synchronized at the origin and at infinity.