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].数学研究及应用,2006,26(2):334~340 |
广义p-Laplace算子相关的非线性边值问题解的存在性 |
Existence of Solution of Nonlinear Boundary Value Problem Involving Generalized p-Laplacian Operator |
投稿时间:2004-05-24 |
DOI:10.3770/j.issn:1000-341X.2006.02.020 |
中文关键词: 增生映射 单调算子 demi连续映射 严格凸空间. |
英文关键词:Accretive mapping monotone operator demi-continuous mapping strictly convex space. |
基金项目:国家自然科学基金(10471003) |
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中文摘要: |
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$L^p(\Omega)$空间中解的存在性,其中$2 \leq p < +\infty $. 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. |
英文摘要: |
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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