非线性分析哲学博士

非线性泛函分析包括从1900年代初开始开发的一系列技术，目的是研究来自分析，几何，物理和应用数学的各种非线性方程。通常，这些技术具有很强的功能分析风格，但数学的许多其他部分（尤其是代数和微分拓扑）的思想也发挥了重要作用。在过去的25年中，非线性泛函分析取得了爆炸性的增长。部分清单包括单调理论，A-proper和凝聚算子，全局分叉理论，从Banach空间或Banach流形中查找实值地图的临界点的新方法，经典Leray-Schauder度的扩展等发展。这些思想在具体非线性问题中的应用。
Nonlinear functional analysis comprises a body of techniques which have been developed since the early 1900's in order to study various nonlinear equations from analysis, geometry, physics and applied mathematics. Typically, these techniques have had a strong functional analytic flavor, but ideas from many other parts of mathematics (notably algebraic and differential topology) have played an important role. The past twenty-five years have seen a particularly explosive growth of nonlinear functional analysis. A partial list includes such developments as the theories of monotone, A-proper and condensing operators, global theories of bifurcation, new methods for finding critical points of real-valued maps from Banach spaces or Banach manifolds, extensions of the classical Leray-Schauder degree and applications of these ideas to concrete nonlinear problems.