Nonlinear functional analysis
Nonlinear functional analysis
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DOI：
10.1090/pspum/018.1
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发表时间：
1970
期刊：
影响因子：
17.1
通讯作者：
F. Browder
中科院分区：
文献类型：
--
作者：
F. Browder
这篇手稿简要介绍了非线性泛函分析。我们从Banach空间中的微积分出发，回顾了微分和积分，(利用一致压缩原理)导出了隐函数定理，并应用这些结果证明了Banach空间中常微分方程解的存在唯一性。其次，在有限(Brouwer度)和无限维(Leray-Schauder度)Banach空间中引入映射度。讨论了博弈论、积分方程组和常微分方程式的几个应用。作为应用，我们考虑偏微分方程解的存在唯一性，证明了定常的N-S方程的解的存在唯一性。最后，我们对单调算子进行了简单的讨论。
This manuscript provides a brief introduction to nonlinear functional analysis. We start out with calculus in Banach spaces, review differentiation and integration, derive the implicit function theorem (using the uniform contraction principle) and apply the result to prove existence and uniqueness of solutions for ordinary differential equations in Banach spaces. Next we introduce the mapping degree in both finite (Brouwer degree) and infinite dimensional (Leray-Schauder degree) Banach spaces. Several applications to game theory, integral equations, and ordinary differential equations are discussed. As an application we consider partial differential equations and prove existence and uniqueness for solutions of the stationary Navier-Stokes equation. Finally, we give a brief discussion of monotone operators.