Methods of nonlinear analysis (非线性分析方法)
发布日期:2007-11-06 浏览次
[内容简介]
In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework, and its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels - a self-contained basic and, organized in appendices, an advanced level for the more experienced reader.
[目次]
Preface.-
1. Preliminaries.-
2. Linear and Nonlinear Operators.-
3. Abstract Integral and Differential Calculus.-
4.- Local Properties of Differentiable Mappings.-
5. Topological and Monotonicity Methods.-
6. Variational Methods.-
7. Boundary Value Problems for PDE.- Summary of Methods.- Typical Applications.- Comparison of Bifurcation Results.- Bibliography.- Index.
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