p-Laplacian问题的一些研究

论文摘要

含有p-Laplacian算子的微分方程边值问题是描述扩散现象的一类拟线性椭圆型微分方程,它出现在数学理论中,在科学技术的各个领域都有着广泛的应用,如气流和海洋运动、人口模型、非线性弹性学和流体动力学等.因此对这个问题的研究不仅具有理论价值,更因其深厚的应用背景而具有实际意义.本文研究p-Laplacian问题正解的存在性,内容分为五章:第一章简单的介绍了p-Laplacian问题的历史背景和研究概况,以及本文的主要工作.第二章介绍了一些基本定义以及本文会用到的基本引理.第三章证明了当非线性项非负（即f（x,z）≥0）时,p-Laplacian问题在超线性情形下正解的存在性.主要通过研究算子的性质、解的凹性和第一特征值的连续性,将边值问题解的存在性转化为算子的不动点存在性进行研究,得到新的结果.第四章首先将f（x,z）≥0推广到了f（x,0）≥0,对f进行了扩张,利用时间算子得到了非负解及正解的存在性.然后又将f（x,0）≥0推广到了f（x,z）∈R,利用一个最大值原理及时间算子的性质得到了正解的存在性.第五章首先总结了本文的主要工作及结论,然后指出了有关本课题今后可以继续研究的方向.在我们的研究中,逐步削弱了对非线性项f的限制,同时克服了算子缺乏线性性质等困难,得到了更大范围内的p-Laplacian问题正解的存在性结果,丰富了这个问题的研究.

论文目录

文章来源

类型: 硕士论文

作者: 李祖艳

导师: 杨光崇

关键词: 问题,正解,存在性,不动点

来源: 成都信息工程大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 成都信息工程大学

分类号: O175.8

DOI: 10.27716/d.cnki.gcdxx.2019.000198

总页数: 51

文件大小: 1338K

下载量: 8

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标签：问题论文;  正解论文;  存在性论文;  不动点论文;