Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers. This book gathers a collection of original articles and state-of-the-art contributions, written by highly distinguished researchers working in differential equations, delay-differential equations, differential inclusions, variational problems, Young measures, control theory, dynamical systems, chaotic systems and their relations with physical systems. The forefront of research in these areas is represented in this volume. The book and all contributions are dedicated to Arrigo Cellina and James A. Yorke on their 65th anniversary. Their remarkable scientific career covered all the above areas and was one of the main driving forces behind the work of many of the authors and the editor of this volume. For researchers and graduate students in mathematics, physics and engineering, the material in this book will be a valuable resource, and a tool for everyone working in differential equations, chaos and variational problems. It brings the reader to the frontiers of research in the areas mentioned above and will stimulate further research.