一类带有负指数的临界椭圆方程组的解

Solutions to a Critical Elliptic System Involving Negative Exponents

研究了一类带有强耦合临界非线性项和负指数项的椭圆方程组.定义了几个重要的约束集,运用复杂的分析技巧研究了能量泛函在约束集的下确界,得到了一个临界常数的精确表达式,最后证明了一定条件下方程组正解的存在性,首次把单个临界椭圆方程的相关结果推广到了带有负指数项的临界椭圆方程组.

In this paper, a system of elliptic equations was investigated, which involves strongly-coupled critical nonlinearities and negative-exponent terms.Several constraint sets were defined, the infimums of the energy functional on the constraint sets were studied by complicated analytical techniques, and the explicit expression of a critical constant was obtained.Finally, the existence of positive solutions to the system was verified under certain conditions, and for the first time, the related conclusions for the single critical elliptic equation were extended to the system of critical elliptic equations involving negative-exponent terms.