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.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
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)
