| 上半空间积分方程组正解的轴对称性 |
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| 引用本文： | 李冬艳. 上半空间积分方程组正解的轴对称性[J]. 纺织高校基础科学学报, 2014, 0(2): 153-157 |
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| 作者姓名： | 李冬艳 |
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| 作者单位： | 西北工业大学应用数学系,陕西西安710129 |
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| 基金项目： | 国家自然科学基金资助项目（11271299）; 陕西省自然科学基础研究计划面上项目（2012JM1014） |
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| 摘 要： | 烄考虑上半空间R+n中积分方程组{u(x)=∫n R+(Gx,y)vq(y)dy,v(x)=∫R+n G(x,y)up(y)d y}正解的性质,其中G(x,y)是具有Dirichlet边界条件的超调和算子(-Δ)m的格林函数.采用积分形式的移动平面法,证明了指数12m p和q之一严格小于1,且在1/p+1+1/q+1+2m/n=1的情形下,方程组正解关于某一平行于xn轴的直线轴对称.
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| 关 键 词： | 积分方程组 积分形式移动平面法 轴对称性 Hardy-Littlewood-Sobolev不等式 |
Rotationally symmetric of positive solutions for system of integral equations on upper half space |
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| LI Dong-yan. Rotationally symmetric of positive solutions for system of integral equations on upper half space[J]. Basic Sciences Journal of Textile Universities, 2014, 0(2): 153-157 |
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| Authors: | LI Dong-yan |
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| Affiliation: | LI Dong-yan (Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710129, China) |
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| Abstract: | The positive solutions for the following system of integral equations in Rn＋：{u（x）=∫n R＋（Gx,y）vq（y）dy,v（x）=∫R＋n G（x,y）up（y）d y}are considered,where G（x,y）is the Green function of the poly-harmonic operator（-Δ）m associated with the Dirichlet boundary value conditions.By using the method of moving planes in integral form,it is proved that every positive solution is rotationally symmetric about some line112 m parallel to the xn-axis when one of the two indices pand qis strictly less than one and 1/p＋1＋1/q＋1＋2m/n=1. |
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| Keywords: | integral equations moving planes in integral form rotationally symmetric Hardy-Littlewood-Sobolev inequality |
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