带有多个临界非线性项的拟线性方程组的解及其渐近性质(英文)

Solutions and Asymptotic Properties of Quasilinear Systems Involving Multiple Critical Nonlinearities

研究了与Caffarelli-Kohn-Nirenberg不等式相关的带有多重临界指数的一类拟线性椭圆方程组,找到了对应的最佳Sobolev常数的极值函数,证明了方程组正解的存在性,同时讨论了这些正解的一些性质.

In this paper, a quasilinear elliptic system is investigated, which involves muhiple critical exponents and the Caffarelli-Kohn-Nirenberg inequality. The extremals of the best Sobolev constants are studied, the existence of positive solutions to the system is proved, some properties of those solutions are also discussed.