INTEGRAL AND FINITE DIFFERENCE INEQUALITIES AND APPLICATIONS

By F. HIUND

CONTENTS INTRODUCTION CHAPTER 1 INTEGRAL INEQUALITIES IN ONE VARIABLE 1 1 INTRODUCTION 1 2 BASIC NONLINEAR INTEGRAL INEQUALITIES 1 3 MORE NONLINEAR INTEGRAL INEQUALITIES 1 4 INEQUALITIES WITH ITERATED INTEGRALS 1 5 BOUNDS ON CERTAIN INTEGRAL INEQUALITIES 1 6 APPLICATIONS 1 6 1 NONLINEAR INTEGRAL AND DIFFERENTIAL EQUATIONS 1 6 2 ITERATED VOLTERRA INTEGRAL EQUATION 1 6 3 GENERAL VOLTERRA-FREDHOLM INTEGRAL EQUATION 1 6 4 TERMINAL VALUE PROBLEM 1 7 NOTES CHAPTER 2 INTEGRAL INEQUALITIES IN TWO VARIABLES 2 1 INTRODUCTION 2 2 SOME NONLINEAR INTEGRAL INEQUALITIES 2 3 FURTHER NONLINEAR INTEGRAL INEQUALITIES 2 4 INEQUALITIES INVOLVING ITERATED INTEGRALS 2 5 ESTIMATES ON SOME INTEGRAL INEQUALITIES 2 6 APPLICATIONS 2 6 1 NONLINEAR PARTIAL DIFFERENTIAL EQUATION 2 6 2 HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TERMINAL VALUES 2 6 3 NON-SELF-ADJOINT HYPERBOLIC PARTIAL FREDHOLM INTEGRODIFFERENTIAL EQUATION 2 6 4 VOLTERRA-FREDHOLM INTEGRAL EQUATION 2 7 NOTES CHAPTER 3 RETARDED INTEGRAL INEQUALITIES 3 1 INTRODUCTION 3 2 BASIC RETARDED INTEGRAL INEQUALITIES IN ONE VARIABLE 3 3 FURTHER RETARDED INTEGRAL INEQUALITIES IN ONE VARIABLE 3 4 RETARDED INTEGRAL INEQUALITIES IN TWO VARIABLES 3 5 MORE RETARDED INTEGRAL INEQUALITIES IN TWO VARIABLES 3 6 APPLICATIONS 3 6 2 RETARDED DIFFERENTIAL AND INTEGRODIFFERENTIAL EQUATIONS 3 6 3 RETARDED PARTIAL DIFFERENTIAL EQUATIONS IN TWO VARIABLES 3 6 4 RETARDED VOLTERRA-FREDHOLM INTEGRAL EQUATION IN TWO VARIABLES 3 7 NOTES CHAPTER 4 FINITE DIFFERENCE INEQUALITIES IN ONE VARIABLE 4 1 INTRODUCTION 4 2 FUNDAMENTAL FINITE DIFFERENCE INEQUALITIES 4 3 SOME MORE FINITE DIFFERENCE INEQUALITIES 4 4 FINITE DIFFERENCE INEQUALITIES WITH ITERATED SUMS 4 5 BOUNDS ON CERTAIN FINITE DIFFERENCE INEQUALITIES 4 6 APPLICATIONS 4 6 1 PERTURBED DIFFERENCE EQUATIONS 4 6 2 VOLTERRA TYPE DIFFERENCE EQUATIONS INVOLVING ITERATED SUMS 4 6 3 VOLTERRA-FREDHOLM TYPE SUM-DIFFERENCE EQUATIONS 4 6 4 FREDHOLM TYPE SUM-DIFFERENCE EQUATIONS 4 7 NOTES CHAPTER 5 FINITE DIFFERENCE INEQUALITIES IN TWO VARIABLES 5 1 INTRODUCTION 5 2 SOME BASIC FINITE DIFFERENCE INEQUALITIES 5 3 FURTHER FINITE DIFFERENCE INEQUALITIES 5 4 ESTIMATES ON CERTAIN FINITE DIFFERENCE INEQUALITIES I 5 5 ESTIMATES ON CERTAIN FINITE DIFFERENCE INEQUALITIES II 5 6 APPLICATIONS 5 6 1 PARTIAL FINITE DIFFERENCE EQUATIONS 5 6 2 VOLTERRA TYPE SUM-DIFFERENCE EQUATION 5 6 3 PARTIAL FINITE SUM-DIFFERENCE EQUATION 5 6 4 SUM-DIFFERENCE EQUATIONS OF VOLTERRA-FREDHOLM TYPE 5 7 NOTES REFERENCES