| 具临界Sobolev指数的半线性椭圆系统的非平凡解 |
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| 引用本文： | 赵培浩,李晓燕,杨德伍.具临界Sobolev指数的半线性椭圆系统的非平凡解[J].兰州大学学报(自然科学版),2002,38(5):1-8. |
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| 作者姓名： | 赵培浩 李晓燕 杨德伍 |
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| 作者单位： | 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 |
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| 基金项目： | Supported by National Natural Science Foundation of China(199710 36 )，Gansu ProvinceNatural Science Foundation(ZS0 2 1- A2 5 - 0 0 2 - Z) |
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| 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 ,并讨论了解的一些性质
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| 关 键 词： | 半线性合作椭圆系统 临界Sobolev指数 非平凡解 |
Nontrivial solution of some semilinear cooperative elliptic systems with critical Sobolev exponent |
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| Abstract.Nontrivial solution of some semilinear cooperative elliptic systems with critical Sobolev exponent[J].Journal of Lanzhou University(Natural Science),2002,38(5):1-8. |
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| Authors: | Abstract |
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| Abstract: | 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. |
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| Keywords: | semilinear cooperative elliptic system critical sobolev exponent nontrivial solution |
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