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Ordinary Differential Equations: 1971 NRL-MRC Conference provides information pertinent to the fundamental aspects of ordinary differential equations. This book covers a variety of topics, including geometric and qualitative theory, analytic theory, functional differential equation, dynamical systems, and algebraic theory. Organized into two parts encompassing 51 chapters, this book begins with an overview of the results on the existence of periodic solutions of a differential equation. This text then describes an index for the isolated invariant sets of a flow on a compact metric space, which contains exactly the information of the Morse index. Other chapters consider the studies of certain classes of equations that can be interpreted as models of biological or economic processes. This book discusses as well the absolute stability of some classes of integro-differential systems. The final chapter deals with first-order differential equations. This book is a valuable resource for mathematicians, graduate students, and research workers.
Language
Place of publication
Publishing group
Elsevier Science & Techn.
ISBN-13
978-1-4832-7011-1 (9781483270111)
Schweitzer Classification
ParticipantsPrefaceI. Invited Papers A General Approach to Linear Problems for Nonlinear Ordinary Differential Equations Differential Relations Conditions for Boundedness of Systems of Ordinary Differential Equations On a Generalization of the Morse Index Equations Modelling Population Growth, Economic Growth, and Gonorrhea Epidemiology Absolute Stability of Some Integro-Differential Systems A New Technique for Proving the Existence of Analytic Functions Potentials with Closed Trajectories on Surfaces of Revolution Local Behavior of Autonomous Neutral Functional Differential Equations External Properties of Biconvex Contingent Equations Asymptotic Distribution of Eigenvalues On Logarithmic Derivatives of Solutions of Disconjugate Linear nth Order Differential Equations Uniqueness and Existence of Solutions of Boundary Value Problems for Ordinary Differential Equations Realization of Continuous-Time Linear Dynamical Systems: Rigorous Theory in the Style of Schwartz Dissipative Systems Relaxation Oscillations and Turbulence Geometric Differential Equations Tauberian Theorems and Functional Equations Perturbations of Volterra Equations Involutory Matrix Differential Equations Control Theory of Hyperbolic Equations Related to Certain Questions in Harmonic Analysis and Spectral Theory (An Outline) The Homology of Invariant Sets of Flows Linear Differential Equations with Delays: Admissibility and Exponential Dichotomies Topological Dynamical Techniques for Differential and Integral Equations Double Asymptotic Expansions for Linear Ordinary Differential Equations Oscillatory Property for Second Order Differential EquationsII. Seminar Papers A Pictorial Study of an Invariant Torus in Phase Space of Four Dimensions Autonomous Perturbations of Some Hamiltonian Systems, All of Whose Solutions Are Periodic Some Boundary Value Problems for Nonlinear Ordinary Differential Equations on Infinite Intervals Positively Stable Dynamical Systems A Nonlinear Predator-Prey Problem Lie Algebras and Linear Differential Equations An Algorithm for Computing Liapunov Functional for Some Differential-Difference Equations Periodic Solutions to Hamiltonian Systems with Infinitely Deep Potential Wells Variational Problems with Delayed Argument Frequency-Domain Criteria for Dissipativity Note on Analytic Solutions of Nonlinear Ordinary Differential Equations at an Irregular Type Singularity Stability of Compactness for Functional Differential Equations Kronecker Invariants and Feedback Lower Bounds and Uniqueness for Solutions of Evolution Inequalities in a Hubert Space Remarks on Linear Differential Equations with Distributional Perturbations Computing Bounds for Focal Points and for s-Points for Second-Order Linear Differential Equations Global Controllability of Nonlinear Systems The Phragmén-Lindelöf Principle and a Class of Functional Differential Equations Singular Perturbations and the Linear State Regulator Problem Delay-Feedback, Time-Optimal, Linear Time-Invariant Control Systems The Family of Direct Periodic Orbits of the First Kind in the Restricted Problem of Three Bodies A General Theory of Liapunov Stability Finite Time Stability of Linear Differential Equations Second Order Oscillation with Retarded Arguments A Note on Malmquist's Theorem on First-Order Differential Equations