| 广义p-Laplace算子相关的非线性边值问题解的存在性 |
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| 引用本文： | 魏利,周海云.广义p-Laplace算子相关的非线性边值问题解的存在性[J].数学研究与评论,2006,26(2):334-340. |
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| 作者姓名： | 魏利 周海云 |
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| 作者单位： | 1. 河北经贸大学数学与统计学学院,河北,石家庄,00061;军械工程学院应用数学与力学研究所,河北,石家庄,060003
2. 军械工程学院应用数学与力学研究所,河北,石家庄,060003;河北师范大学数学与信息科学学院,河北,石家庄,050016 |
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| 基金项目： | 国家自然科学基金(10471003) |
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| 摘 要： | 本文首先把p-Laplace算子推广为广义p-Laplace算子,然后利用非线性增生映射值域的扰动理论研究了与广义p-Laplace算子相关的具有牛曼边值的非线性椭圆问题在LP(Ω)空间中解的存在性,其中2≤p< ∞．本文所讨论的方程及所用的方法是对以往一些工作的补充和延续．
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| 关 键 词： | 增生映射 单调算子 demi连续映射 严格凸空间 |
| 文章编号： | 1000-341X(2006)02-0334-07 |
| 收稿时间： | 05 24 2004 12:00AM |
| 修稿时间： | 2004年5月24日 |
Existence of Solution of Nonlinear Boundary Value Problem Involving Generalized p-Laplacian Operator |
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| WEI Li and ZHOU Hai-yun.Existence of Solution of Nonlinear Boundary Value Problem Involving Generalized p-Laplacian Operator[J].Journal of Mathematical Research and Exposition,2006,26(2):334-340. |
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| Authors: | WEI Li and ZHOU Hai-yun |
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| Institution: | School of Math. & Stat., Hebei University of Economics and Business, Shijiazhuang 050061, China; Inst. of Appl. Math. & Mech., Ordnance Engineering College, Shijizhuang 050003, China;Inst. of Appl. Math. & Mech., Ordnance Engineering College, Shijizhuang 050003, China; Inst. of Math. & Inform. Sci., Hebei Normal University, Shijizhuang 050016, China |
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| Abstract: | In this paper, the $p$-Laplacian operator is generalized to the generalized $p$-Laplacian operator. Then, the perturbation results of the ranges of nonlinear accretive mappings are used to discuss, the existence of the solution of the nonlinear elliptic problem with Neumann boundary value involving the generalized $p$-Laplacian operator in $L^p(\Omega)$ space, $2 \leq p < + \infty$. The equations and methods here are continuation and complement to some previous works. |
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| Keywords: | Accretive mapping monotone operator demi-continuous mapping strictly convex space |
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