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 reseach, 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. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real world applications - Written for mathematicians and scientists of many related fields

Functional differential equations have received attention since the 1920's. Within that development, boundary value problems have played a prominent role in both the theory and applications dating back to the 1960's. This book attempts to present some of the more recent developments from a cross-section of views on boundary value problems for functional differential equations.Contributions represent not only a flavor of classical results involving, for example, linear methods and oscillation-nonoscillation techiques, but also modern nonlinear methods for problems involving stability and control as well as cone theoretic, degree theoretic, and topological transversality strategies. A balance with applications is provided through a number of papers dealing with a pendulum with dry friction, heat conduction in a thin stretched resistance wire, problems involving singularities, impulsive systems, traveling waves, climate modeling, and economic control.With the importance of boundary value problems for functional differential equations in applications, it is not surprising that as new applications arise, modifications are required for even the definitions of the basic equations. This is the case for some of the papers contributed by the Perm seminar participants. Also, some contributions are devoted to delay Fredholm integral equations, while a few papers deal with what might be termed as boundary value problems for delay-difference equations.

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.