Ordinary and Delay Differential Equations

This Research Note reflects the contemporary achievements and problems in the theory and applications of ordinary and delay differential equations, summarizes recent results and methods, and emphasizes new ideas and directions for future research activity. A distinct feature of the volume is that it contains considerable contributions to the field of differential equations in both real and complex domains. Readers interested in the qualitative theory of ordinary differential equations and dynamical systems will find here important papers on homoclinic and periodic solutions in conservative and reversible systems, rotated vector fields and homoclinic loop bifurcations, bifurcation sets and limit cycles, gradient systems, and invariant manifolds. Several articles contain significant contributions to the stability theory of ordinary and functional differential equations. A number of strong results crowns the efforts of authors concerned with the oscillatory properties of ordinary differential, functional differential, and difference equations. Specialists in the analytical theory of differential equations and complex analysis will enjoy the material on Gevrey asymptotics, solutions of maximal growth satisfying linear differential equations, formal solutions of nonlinear systems, series of Dirac delta functions, and other topics. The book also includes contributions on equations that represent biological or technical models. In summary, this volume will be invaluable for applied mathematicians, scientists, engineers, and any researcher concerned with dynamical systems. Aimed at researchers and graduate students in the field of differential equations, dynamical systems, and their applications.