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.

Zusammenfassung

This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Inhalt
Nodal and Multiple Constant Sign Solution for Equations with the p-Laplacian.- A Young Measures Approach to Averaging.- Viability Kernels and Capture Basins for Analyzing the Dynamic Behavior: Lorenz Attractors, Julia Sets, and Hutchinson's Maps.- Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.- On the Euler-Lagrange Equation for a Variational Problem.- Singular Limits for Impulsive Lagrangian Systems with Dissipative Sources.- Lipschitz Continuity of Optimal Trajectories in Deterministic Optimal Control.- An Overview on Existence of Vector Minimizers for Almost Convex 1dim Integrals.- Strict Convexity, Comparison Results and Existence of Solutions to Variational Problems.- Necessary Optimality Conditions for Discrete Delay Inclusions.- Necessary Conditions in Optimal Control and in the Calculus of Variations.- Almost Periodicity in Functional Equations.- Age-dependent Population Dynamics with the Delayed Argument.- Chaos in the Störmer Problem.- Hausdorff Dimension versus Smoothness.- On Bounded Trajectories for Some Non-Autonomous Systems.- On Generalized Differential Quotients and Viability.- Nonlinear Prediction in Riverflow the Paiva River Case.- Shadowing in Higher Dimensions.- Boundary Value Problems for Nonlinear Perturbations of Singular ?-Laplacians.- Existence, Nonexistence and Multiplicity Results for Some Beam Equations.- Reducing a Differential Game to a Pair of Optimal Control Problems.- Optimal Control of Nonconvex Differential Inclusions.- On Chaos of a Cubic p-adic Dynamical System.- Some New Concepts of Dimension.- Degree Theory and Almost Periodic Problems.- L ?-Energy Method, Basic Tools and Usage.- On the Singular Set of Certain Potential Operators in Hilbert Spaces.- Shape and Conley Indexof Attractors and Isolated Invariant Sets.- Regularity of Solutions for the Autonomous Integrals of the Calculus of Variations.- Multi-modal Periodic Trajectories in Fermi-Pasta-Ulam Chains.- Control of Transient Chaos Using Safe Sets in Simple Dynamical Systems.