具临界 Sobolev指数的半线性椭圆系统的非平凡解(英文)  

Nontrivial solution of some semilinear cooperative elliptic systems with critical Sobolev exponent

作　　者：赵培浩[1] 李晓燕[2] 杨德伍[2] 

机构地区：[1]兰州大学数学系,甘肃兰州730000 [2]河南科技大学数理系,河南洛阳471003

出　　处：《兰州大学学报（自然科学版）》2002年第5期1-8,共8页Journal of Lanzhou University(Natural Sciences)

基　　金：Supported by National Natural Science Foundation of China(199710 36 ) ;Gansu ProvinceNatural Science Foundation(ZS0 2 1- A2 5 - 0 0 2 - Z)

摘　　要：讨论了具临界 Sobolev指数的半线性椭圆系统的非平凡解的存在性 .通过使用没有 (PS)条件的极小极大定理 ,以及对最佳 Sobolev嵌入常数的详细分析 ,得到了一些具临界 Sobolev指数的半线性椭圆系统的真正非平凡解的存在性 。This paper deals with the existence of nontrivial solutions of some semilinear cooperative elliptic systems involving critical Sobolev exponent. It is well-known that one of the most important problem of elliptic system is to find the really nontrivial solution. Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without (PS) conditions.In fact,the solution we obtained here is really nontrivial in the sense of every unknown functions being nontrivial.

关 键 词：半线性合作椭圆系统 临界SOBOLEV指数 非平衡解 极大极小定理 最佳Sobolev嵌入常数 

分 类 号：O175.25[理学—数学] O241[理学—基础数学]