Ordinary differential equations : 1971 NRL-MRC conference : proceedings of a conference on ordinary differential equations, sponsored by the Mathematics Research Center of the Naval Research Laboratory, held in Washington, D.C., June 14-23, 1971

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. Content: Front Matter, Page iii Copyright, Page iv PARTICIPANTS, Pages ix-xii PREFACE, Page xiii, Leonard Weiss A GENERAL APPROACH TO LINEAR PROBLEMS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS, Pages 3-9, H.A. Antosiewicz DIFFERENTIAL RELATIONS, Pages 11-17, D. Bushaw CONDITIONS FOR BOUNDEDNESS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS, Pages 19-26, M.L. Cartwright ON A GENERALIZATION OF THE MORSE INDEX, Pages 27-33, C. Conley EQUATIONS MODELLING POPULATION GROWTH, ECONOMIC GROWTH, AND GONORRHEA EPIDEMIOLOGY, Pages 35-53, Kenneth L. Cooke, James A. Yorke ABSOLUTE STABILITY OF SOME INTEGRO-DIFFERENTIAL SYSTEMS, Pages 55-70, C. Corduneanu A NEW TECHNIQUE FOR PROVING THE EXISTENCE OF ANALYTIC FUNCTIONS, Pages 71-81, Stephen P. Diliberto POTENTIALS WITH CLOSED TRAJECTORIES ON SURFACES OF REVOLUTION, Pages 83-93, A. Halanay LOCAL BEHAVIOR OF AUTONOMOUS NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS, Pages 95-107, Jack K. Hale EXTREMAL PROPERTIES OF BICONVEX CONTINGENT EQUATIONS, Pages 109-119, Hubert Halkin ASYMPTOTIC DISTRIBUTION OF EIGENVALUES, Pages 121-125, W.A. Harris Jr., Y. Sibuya ON LOGARITHMIC DERIVATIVES OF SOLUTIONS OF DISCONJUGATE LINEAR nTH ORDER DIFFERENTIAL EQUATIONS, Pages 127-136, Philip Hartman UNIQUENESS AND EXISTENCE OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS, Pages 137-149, Lloyd K. Jackson REALIZATION OF CONTINUOUS-TIME LINEAR DYNAMICAL SYSTEMS: RIGOROUS THEORY IN THE STYLE OF SCHWARTZ, Pages 151-164, R.E. Kalman, M.L.J. Hautus DISSIPATIVE SYSTEMS, Pages 165-174, J.P. LaSalle RELAXATION OSCILLATIONS AND TURBULENCE, Pages 175-183, A. Lasota GEOMETRIC DIFFERENTIAL EQUATIONS, Pages 185-193, Solomon Lefschetz TAUBERIAN THEOREMS AND FUNCTIONAL EQUATIONS, Pages 195-207, J.J. Levin, D.F. Shea PERTURBATIONS OF VOLTERRA EQUATIONS, Pages 209-219, John A. Nohel INVOLUTORY MATRIX DIFFERENTIAL EQUATIONS, Pages 221-240, William T. Reid CONTROL THEORY OF HYPERBOLIC EQUATIONS RELATED TO CERTAIN QUESTIONS IN HARMONIC ANALYSIS AND SPECTRAL THEORY: (An Outline), Pages 241-263, David L. Russell THE HOMOLOGY OF INVARIANT SETS OF FLOWS, Pages 265-275, Robert J. Sacker LINEAR DIFFERENTIAL EQUATIONS WITH DELAYS: ADMISSIBILITY AND EXPONENTIAL DICHOTOMIES, Pages 277-286, J.J. Schäffer TOPOLOGICAL DYNAMICAL TECHNIQUES FOR DIFFERENTIAL AND INTEGRAL EQUATIONS, Pages 287-304, George R. Sell DOUBLE ASYMPTOTIC EXPANSIONS FOR LINEAR ORDINARY DIFFERENTIAL EQUATIONS, Pages 305-314, Wolfgang Wasow OSCILLATORY PROPERTY FOR SECOND ORDER DIFFERENTIAL EQUATIONS, Pages 315-327, Taro Yoshizawa A PICTORIAL STUDY OF AN INVARIANT TORUS IN PHASE SPACE OF FOUR DIMENSIONS, Pages 331-349, R. Baxter, H. Eiserike, A. Stokes AUTONOMOUS PERTURBATIONS OF SOME HAMILTONIAN SYSTEMS, ALL OF WHOSE SOLUTIONS ARE PERIODIC, Pages 351-357, Melvyn S. Berger SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVALS, Pages 359-363, Melvyn S. Berger POSITIVELY STABLE DYNAMICAL SYSTEMS, Pages 365-370, Nam P. Bhatia A NONLINEAR PREDATOR-PREY PROBLEM, Pages 371-377, Fred Brauer LIE ALGEBRAS AND LINEAR DIFFERENTIAL EQUATIONS, Pages 379-386, Roger W. Brockett, Abdolhossein Rahimi AN ALGORITHM FOR COMPUTING LIAPUNOV FUNCTIONALS FOR SOME DIFFERENTIAL-DIFFERENCE EQUATIONS, Pages 387-398, Richard Datko PERIODIC SOLUTIONS TO HAMILTONIAN SYSTEMS WITH INFINITELY DEEP POTENTIAL WELLS, Pages 399-403, William B. Gordon VARIATIONAL PROBLEMS WITH DELAYED ARGUMENT, Pages 405-412, A. Halanay FREQUENCY-DOMAIN CRITERIA FOR DISSIPATIVITY, Pages 413-417, A. Halanay NOTE ON ANALYTIC SOLUTIONS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS AT AN IRREGULAR TYPE SINGULARITY, Pages 419-431, P.F. Hsieh STABILITY OF COMPACTNESS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS, Pages 433-458, G. Stephen Jones KRONECKER INVARIANTS AND FEEDBACK, Pages 459-471, R.E. Kaiman LOWER BOUNDS AND UNIQUENESS FOR SOLUTIONS OF EVOLUTION INEQUALITIES IN A HILBERT SPACE, Pages 473-487, G. Ladas, V. Lakshmikantham REMARKS ON LINEAR DIFFERENTIAL EQUATIONS WITH DISTRIBUTIONAL PERTURBATIONS, Pages 489-495, A. Lasota COMPUTING BOUNDS FOR FOCAL POINTS AND FOR σ-POINTS FOR SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS, Pages 497-503, Walter Leighton GLOBAL CONTROLLABILITY OF NONLINEAR SYSTEMS, Pages 505-512, D.L. Lukes THE PHRAGMÉN-LINDELÖF PRINCIPLE AND A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS, Pages 513-540, Grainger R. Morris, Alan Feldstein, Ernie W. Bowen SINGULAR PERTURBATIONS AND THE LINEAR STATE REGULATOR PROBLEM, Pages 541-544, R.E. O'Malley Jr. DELAY-FEEDBACK, TIME-OPTIMAL, LINEAR TIME-INVARIANT CONTROL SYSTEMS, Pages 545-552, V.M. Popov THE FAMILY OF DIRECT PERIODIC ORBITS OF THE FIRST KIND IN THE RESTRICTED PROBLEM OF THREE BODIES, Pages 553-561, Dieter S. Schmidt A GENERAL THEORY OF LIAPUNOV STABILITY, Pages 563-568, P. Seibert FINITE TIME STABILITY OF LINEAR DIFFERENTIAL EQUATIONS, Pages 569-580, Leonard Weiss, Jong-Sen Lee SECOND ORDER OSCILLATION WITH RETARDED ARGUMENTS, Pages 581-596, James S.W. Wong A NOTE ON MALMQUIST'S THEOREM ON FIRST-ORDER DIFFERENTIAL EQUATIONS, Pages 597-607, Chung-Chun Yang Edited By Leonard Weiss. Proceedings Of A Conference Sponsored By The Mathematics Research Center Of The Naval Research Laboratory, Held In Washington, D.c., June 14-23, 1971. Includes Bibliographies.