Mathematics and Its Applications398- Existence Theory for Nonlinear Ordinary Differential Equations

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. Familiar examples show that the interval of existence can be arbi­ trarily short, depending on the initial value r and the nonlinear behaviour of I.



This book presents an up-to-date account of many topics of current interest in the theory of nonlinear ordinary differential equations. Topics include fixed point theory, periodic problems, lower and upper surfaces, positone and semi-positone problems, singular equations, limit circle problems, finite and infinite interval problems, and impulsive differential equations. In addition many important applications are presented to complement the theory. Audience: This work will be of interest to theoretical and applied mathematicians, and graduate students in the above disciplines.