TITLE PAGE -- TABLE OF CONTENTS -- PREFACE -- ACKNOWLEDGMENTS -- 1 INTRODUCTION, CLASSIFICATION, SHORT HISTORY, AUXILIARY RESULTS, AND METHODS -- 1.1 CLASSICAL AND NEW TYPES OF FEs -- 1.2 MAIN DIRECTIONS IN THE STUDY OF FDE -- 1.3 METRIC SPACES AND RELATED CONCEPTS -- 1.4 FUNCTIONS SPACES -- 1.5 SOME NONLINEAR AUXILIARY TOOLS -- 1.6 FURTHER TYPES OF FES -- 2 EXISTENCE THEORY FOR FUNCTIONAL EQUATIONS -- 2.1 LOCAL EXISTENCE FOR CONTINUOUS OR MEASURABLE SOLUTIONS -- 2.2 GLOBAL EXISTENCE FOR SOME CLASSES OF FUNCTIONAL DIFFERENTIAL EQUATIONS -- 2.3 EXISTENCE FOR A SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATION -- 2.4 THE COMPARISON METHOD IN OBTAINING GLOBAL EXISTENCE RESULTS -- 2.5 A FUNCTIONAL DIFFERENTIAL EQUATION WITH BOUNDED SOLUTIONS ON THE POSITIVE SEMIAXIS -- 2.6 AN EXISTENCE RESULT FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH RETARDED ARGUMENT -- 2.7 A SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH BOUNDED SOLUTIONS ON THE POSITIVE SEMIAXIS -- 2.8 A GLOBAL EXISTENCE RESULT FOR A CLASS OF FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS -- 2.9 A GLOBAL EXISTENCE RESULT IN A SPECIAL FUNCTION SPACE AND A POSITIVITY RESULT -- 2.10 SOLUTION SETS FOR CAUSAL FUNCTIONAL DIFFERENTIAL EQUATIONS -- 2.11 AN APPLICATION TO OPTIMAL CONTROL THEORY -- 2.12 FLOW INVARIANCE -- 2.13 FURTHER EXAMPLES/APPLICATIONS/COMMENTS -- 2.14 BIBLIOGRAPHICAL NOTES -- 3 STABILITY THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS -- 3.1 SOME PRELIMINARY CONSIDERATIONS AND DEFINITIONS -- 3.2 COMPARISON METHOD IN STABILITY THEORY OF ORDINARY DIFFERENTIAL EQUATIONS -- 3.3 STABILITY UNDER PERMANENT PERTURBATIONS -- 3.4 STABILITY FOR SOME FUNCTIONAL DIFFERENTIAL EQUATIONS -- 3.5 PARTIAL STABILITY -- 3.6 STABILITY AND PARTIAL STABILITY OF FINITE DELAY SYSTEMS -- 3.7 STABILITY OF INVARIANT SETS -- 3.8 ANOTHER TYPE OF STABILITY -- 3.9 VECTOR AND MATRIX LIAPUNOV FUNCTIONS.

3.10 A FUNCTIONAL DIFFERENTIAL EQUATION -- 3.11 BRIEF COMMENTS ON THE START AND EVOLUTION OF THE COMPARISON METHOD IN STABILITY -- 3.12 BIBLIOGRAPHICAL NOTES -- 4 OSCILLATORY MOTION, WITH SPECIAL REGARD TO THE ALMOST PERIODIC CASE -- 4.1 TRIGONOMETRIC POLYNOMIALS AND APr-SPACES -- 4.2 SOME PROPERTIES OF THE SPACES -- 4.3 APr-SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS -- 4.4 APr-SOLUTIONS TO CONVOLUTION EQUATIONS -- 4.5 OSCILLATORY SOLUTIONS INVOLVING THE SPACE B -- 4.6 OSCILLATORY MOTIONS DESCRIBED BY CLASSICAL ALMOST PERIODIC FUNCTIONS -- 4.7 DYNAMICAL SYSTEMS AND ALMOST PERIODICITY -- 4.8 BRIEF COMMENTS ON THE DEFINITION OF SPACES AND RELATED TOPICS -- 4.9 BIBLIOGRAPHICAL NOTES -- 5 NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS -- 5.1 SOME GENERALITIES AND EXAMPLES RELATED TO NEUTRAL FUNCTIONAL EQUATIONS -- 5.2 FURTHER EXISTENCE RESULTS CONCERNING NEUTRAL FIRST-ORDER EQUATIONS -- 5.3 SOME AUXILIARY RESULTS -- 5.4 A CASE STUDY, I -- 5.5 ANOTHER CASE STUDY, II -- 5.6 SECOND-ORDER CAUSAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS, I -- 5.7 SECOND-ORDER CAUSAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS, II -- 5.8 A NEUTRAL FUNCTIONAL EQUATION WITH CONVOLUTION -- 5.9 BIBLIOGRAPHICAL NOTES -- APPENDIX A: ON THE THIRD STAGE OF FOURIER ANALYSIS -- A.1 INTRODUCTION -- A.2 RECONSTRUCTION OF SOME CLASSICAL SPACES -- A.3 CONSTRUCTION OF ANOTHER CLASSICAL SPACE -- A.4 CONSTRUCTING SPACES OF OSCILLATORY FUNCTIONS: EXAMPLES AND METHODS -- A.5 CONSTRUCTION OF ANOTHER SPACE OF OSCILLATORY FUNCTIONS -- A.6 SEARCHING FUNCTIONAL EXPONENTS FOR GENERALIZED FOURIER SERIES -- A.7 SOME COMPACTNESS PROBLEMS -- BIBLIOGRAPHY -- INDEX -- PURE AND APPLIED MATHEMATICS -- END USER LICENSE AGREEMENT.