Handbook of Differential Equations: Ordinary Differential Equations, Volume 1 (Handbook of Differential Equations)

Main subject categories: • Ordinary differential equations • Differential equations • Initial value problems • Boundary value problems • Half-linear differential equations • Radial solutions of quasilinear elliptic differential equations • Integrability of polynomial differential systems • Global results for the forced pendulum equation • Ważewski method and Conley indexThe book contains seven survey papers about ordinary differential equations. The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling ‒ nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations. The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications. The book contains seven survey papers about ordinary differential equations.

The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.

The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications. This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for research, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume This handbook is the fourth volume in a series of volumes devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.* Covers a variety of problems in ordinary differential equations * Pure mathematical and real world applications * Written for mathematicians and scientists of many related fields The study of singular boundary value problems (singular in the dependent variable) is relatively new.