| R~N空间中退化的logistic型拟线性椭圆方程正解存在唯一性 |
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| 引用本文： | 董卫,郭长河,张清年,时翠梅.R~N空间中退化的logistic型拟线性椭圆方程正解存在唯一性[J].数学学报,2006,49(4):861-868. |
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| 作者姓名： | 董卫 郭长河 张清年 时翠梅 |
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| 作者单位： | 河北工程大学,邯郸056021 |
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| 基金项目： | 河北省自然科学基金资助项目（A2006000605） |
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| 摘 要： | 本文研究下列退化的logistic型p-Laplacian方程:-△Apu=a(x)|u|p-2u- b(x)|u|q-1u,x∈RN(N≥2)．在对系数a(x),b(x)在无穷远处的性质加以一般限制,得出了正解唯一存在性定理．我们的结果改进了文1]和2]中的相应结果．
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| 关 键 词： | 退化的logistic 拟线性椭圆方程 边界爆破解 |
| 文章编号： | 0583-1431（2006）04-0861-08 |
| 收稿时间： | 2005-01-11 |
| 修稿时间： | 2005-01-112005-07-15 |
Uniqueness and Existence of Positive Solutions for Degenerate Logistic Type Quasilinear Elliptic Equations on R~N |
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| Wei DONG, Chang He GUO, Qing Nian ZHANG, Cui Mei SHI.Uniqueness and Existence of Positive Solutions for Degenerate Logistic Type Quasilinear Elliptic Equations on R~N[J].Acta Mathematica Sinica,2006,49(4):861-868. |
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| Authors: | Wei DONG Chang He GUO Qing Nian ZHANG Cui Mei SHI |
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| Institution: | Hebei University of Engineering, Handan 056021, P. R. China |
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| Abstract: | In this paper, we consider positive solutions of the degenerate logistic type p-Laplacian equation -△pu =a(x)|u|p-2u-b(x)|u|q-1u,x∈RN (N≥2). We show that under rather general conditions on a(x) and b(x) for large |x|, there exists a unique positive solution. Our results improve the corresponding ones in 1] and 2]. |
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| Keywords: | degenerate logistic type quasilinear lliptic equations boundary blow-up solution |
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