Differential Equations, Choas and Variational

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 purpose of the volume is to bring 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. It treats the nonlinear aspects of the theory of differential equations, of the calculus of variations, dynamical systems, as well as topics related to chaotic systems and their relations with physical problems. The reader will find both some surveys of the more recent developments in several topics related with differential equations, chaos and variational problems, as well as new contributions in active and important areas of research as Young measures, optimal control, differential and delay-differential equations and inclusions.

Editorial Introduction	p. ix
Nodal and Multiple Constant Sign Solution for Equations with the p-Laplacian	p. 1
A Young Measures Approach to Averaging	p. 15
Viability Kernels and Capture Basins for Analyzing the Dynamic Behavior: Lorenz Attractors, Julia Sets, and Hutchinson's Maps	p. 29
Generahzed Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis	p. 49
On the Euler-Lagrange Equation for a Variational Problem	p. 61
Singular Limits for Impulsive Lagrangian Systems with Dissipative Sources	p. 79
Lipschitz Continuity of Optimal Trajectories in Deterministic Optimal Control	p. 105
An Overview on Existence of Vector Minimizers for Almost Convex 1-dim Integrals	p. 117
Strict Convexity, Comparison Results and Existence of Solutions to Variational Problems	p. 123
Necessary Optimality Conditions for Discrete Delay Inclusions	p. 135
Necessary Conditions in Optimal Control and in the Calculus of Variations	p. 143
Almost Periodicity in Functional Equations	p. 157
Age-dependent Population Dynamics with the Delayed Argument	p. 165
Chaos in the Störmer Problem	p. 175
Hausdorff Dimension versus Smoothness	p. 195
On Bounded Trajectories for Some Non-Autonomous Systems	p. 211
On Generalized Differential Quotients and Viability	p. 223
Nonlinear Prediction in Riverflow - the Paiva River Case	p. 231
Shadowing in Higher Dimensions	p. 241
Boundary Value Problems for Nonlinear Perturbations of Singular ¿-Laplacians	p. 247
Existence, Nonexistence and Multiplicity Results for Some Beam Equations	p. 257
Reducing a Differential Game to a Pair of Optimal Control Problems	p. 269
Optimal Control of Nonconvex Differential Inclusions	p. 285
On Chaos of a Cubic p-adic Dynamical System	p. 305
Some New Concepts of Dimension	p. 317
Degree and Almost Periodicity	p. 345
L^∞-Energy Method, Basic Tools and Usage	p. 357
Singular Set of Certain Potential Operators in Hilbert Spaces	p. 377
Shape and Conley Index of Attractors and Isolated Invariant Sets	p. 393
Regularity of Solutions for the Autonomous Integrals of the Calculus of Variations	p. 407
Multi-modal Periodic Trajectories in Fermi-Pasta-Ulam Chains	p. 415
Control of Transient Chaos Using Safe Sets in Simple Dynamical Systems	p. 425
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Differential Equations, Choas and Variational Problems

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