含临界Sobolev指数的非线性椭圆方程解的存在性

THE EXISTENCE OF THE NONTRIVAL SOLUTION FOR A NONLINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

通过构造一个新的函数来讨论包含Ｓｏｂｏｌｅｖ指数的椭圆方程的非平凡解的存在性，我们证明了当Ω是关于原点的星形域时，方程（１）不存在非平凡解。

in this paper, we discuss the existence of the nontrivial solution for a nonlinear elliptic equations involving critical Sobolev exponents via constructing a new function. We also prove that equaton (1) has no nontrival solution when Ω is starshapedwith respect to the origin.