zbMATH — the first resource for mathematics

Nonlinear boundary value problems for ordinary differential equations. (English) Zbl 0615.34010
There are six chapters and their coverage is as follows. Chapter I: Prerequisite and background on the topological and other techniques used throughout the text. Chapter II: Existence and uniqueness problems for the equation \(y''=f(t,y,y')\) together with a variety of boundary conditions which include the Dirichlet, Neumann, periodic and Sturm- Liouville conditions. Chapter III: Applications of chapter II results to a variety of practical problems which arise often. Chapter IV: Other second, order boundary value problems such as periodic solutions of Nirenberg type, Dirichlet problem for \(y''=f(y')\), Neumann problem for \(y''=f(t,y,y')\), upper and lower solutions. Chapter V: Extensions of results and techniques to even order systems and higher order equations. Chapter VI: Numerical solution of some boundary value problems illustrated with the following methods: Newton’s Dirichlet and Neumann methods, the shooting method and the quasilinearization method. The treatment here only discusses the methods, and actual computations are not given.
Reviewer: J.O.C.Ezeilo

34B15 Nonlinear boundary value problems for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations