FUNCTIONAL EQUATIONS WITH CAUSAL OPERATORS

By V. JANAI

CONTENTS INTRODUCTION CLASSES OF FUNCTIONAL EQUATIONS EQUATIONS WITH CAUSAL OPERATORS CAUSAL OPERATORS IN APPLICATIONS AUXILIARY CONCEPTS ABSTRACT SPACES FUNCTION SPACES OPERATORS ON FUNCTION SPACES FIXED POINTS AND OTHER AUXILIARY RESULTS EXISTENCE THEORY FOR FUNCTIONAL EQUATIONS WITH CAUSAL OPERATORS THE EQUATION X(T) = (V X)(T) IN THE SPACE OF CONTINUOUS FUNCTIONS THE EQUATION X(T) = (V X)(T) IN SPACES OF MEASURABLE FUNCTIONS EXISTENCE AND APPROXIMATION OF SOLUTIONS BY MEANS OF THE SINGULAR PERTURBATION TECHNIQUE GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL EQUATIONS WITH CAUSAL OPERATORS SOME GLOBAL RESULTS OF EXISTENCE AND UNIQUENESS FUNCTIONAL INEQUALITIES INITIAL VALUE PROBLEMS OF THE SECOND KIND FOR FUNCTIONAL DIFFERENTIAL EQUATIONS LINEAR AND QUASILINEAR EQUATIONS WITH CAUSAL OPERATORS GLOBAL EXISTENCE AND UNIQUENESS FOR LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS GLOBAL EXISTENCE AND UNIQUENESS FOR LINEAR FUNCTIONAL EQUATIONS INTEGRAL REPRESENTATION OF SOLUTIONS OF LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS INITIAL VALUE PROBLEMS WITH FUNCTIONAL DATA FOR LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS QUASILINEAR FUNCTIONAL EQUATIONS TWO-POINT BOUNDARY VALUE PROBLEMS COMMENTS AND REFERENCES STABILITY THEORY DE?NITION AND GENERALITIES STABILITY OF LINEAR SYSTEMS STABILITY OF QUASILINEAR SYSTEMS COMPARISON METHOD IN STABILITY ADMISSIBILITY CONCEPTS NEUTRAL FUNCTIONAL EQUATIONS THE CONCEPT OF NEUTRAL FUNCTIONAL EQUATION WITH CAUSAL OPERATORS EXISTENCE RESULTS IN THE CONTINUOUS CASE EXISTENCE RESULTS IN SPACES OF MEASURABLE FUNCTIONS MORE RESULTS ON NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS THE LINEAR AND QUASILINEAR CASES MISCELLANEA (APPLICATIONS AND GENERALIZATIONS) A LINEAR–QUADRATIC OPTIMAL CONTROL PROBLEM WITH CAUSAL OPERATORS A MAXIMUM PRINCIPLE APPROACH ASYMPTOTIC BEHAVIOR IN SECOND-ORDER SYSTEMS GLOBAL EXISTENCE FOR THE EQUATION X(T) = (LX)(T) + (NX)(T) REVIEW OF FURTHER RESULTS AND TOPICS REFERENCES