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 1-dim 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 Index of 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.

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.