拟线性椭圆算子的(S)+性质与p(x)-Laplacian型方程

兰州大学机构库 >数学与统计学院

	拟线性椭圆算子的(S)+性质与p(x)-Laplacian型方程
Alternative Title	(S)+-property of quasilinear elliptic operators and equations of p(x)-Laplacian type
	关春霞
Thesis Advisor	范先令
	2008-05-26
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	Musielak-Orlicz 空间一致凸性 (S)+ 型映射拟线性椭圆算子 p(x)-Laplacian 型方程
Abstract	本文中在较弱的条件下对向量值Musielak-Orlicz 空间的一些已有的理论结果进行了改进, 并给出了在此类一致凸空间上的Radon-Riesz 定理的一个有用的变体; 研究了由Musielak-Orlicz 函数生成的凸模的性质, 用Musielak-Orlicz 函数的一致凸性给出了由它生成的凸模的次微分映射是(S)+型映射的一个充分条件; 在此理论基础上, 证明了很广的一类具变分结构的拟线性椭圆算子是(S)+型的; 引入了具有变指数p(x)型的Musielak-Orlicz 函数及p(x)-Laplacian 型算子的新概念, 它包含通常的p(x)-Laplacian 算子为其特殊情形, 证明了p(x)-Laplacian 型算子是(S)+型的;获得了一批关于p(x)-Laplacian 型方程解的存在性与多解性的结果. 本文中所提出的p(x)-Laplacian 型算子的概念及获得的相关结果是对由De N´apoli 和Mariani 提出的p-Laplacian 型算子及相应结果的本质性的改进和发展.
Other Abstract	In this paper, under some weaker conditions we have improved some theories of the vector valued Musielak-Orlicz spaces and give some useful variants of Radon-Riesz theorem in the uniformly convex spaces. We studies the property of the convex modular which is generated by a Musielak-Orlicz function, using the uniform convexity of the Musielak- Orlicz function, we give a sufficient condition for the (S)+-property of the subdifferential mapping of the convex modular generated by it; And based on this we obtain the (S)+-property of a wide class of the quasilinear elliptic operators with the variational structure.We introduce the new notion of a special subclass of the Musielak-Orlicz function, which is called of type with variable exponent, and the p(x)-Laplacian type operators which include the p(x)-Laplacian operator as a special case. We have showed the (S)+-property of the p(x)-Laplacian type operators. As an application of this result, we obtain the existence and multiplicity of solutions for the class of equations of the p(x)-Laplacian type. The notion of p(x)-Laplacian type operators and the results obtained in this paper are the essence of the improvement and development of p-Laplacian type operators and the corresponding results in [10] by De N´apoli and Mariani .
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224834
Collection	数学与统计学院
Recommended Citation GB/T 7714	关春霞. 拟线性椭圆算子的(S)+性质与p(x)-Laplacian型方程[D]. 兰州. 兰州大学,2008.

Files in This Item:
There are no files associated with this item.

If you have any objections to this item, please fill out the form below and the administrator will contact you as soon as possible.
Content:
Email：	*
Institution:
Verification Code:	Refresh

Any comments and suggestions are welcomed.
Title:	*
Content:
Email：	*
Verification Code:	Refresh

数学与统计学院知识库