Nonlinear boundary value problems for ordinary differential equations.

*(English)*Zbl 0615.34010There 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

##### MSC:

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 |