Differential equations and integral inequalities with ¿maximum¿

The main aim of the book is study of integral inequalities and differential equations in the special case when the value of the unknown function is involved not only at the present time but also its maximal value on a past time interval is presented. Initially several types of integral inequalities with ¿maximum¿ for continuous and piecewise continuous functions are solved. This helps us to build the mathematical apparatus for qualitative investigation of the behavior of the solutions of differential equations with ¿maximum¿. Several types of sufficient conditions for uniqueness, boundedness, continuous dependence on the initial conditions and stability of the solutions are obtained. Much of the material presented in this book is based on the recent research of authors on the topic. The current book is intended for a wide audience, including Mathematicians, Applied Researchers, and Practitioners, whose interest extends beyond the boundaries of qualitative analysis of differential equations and the modeling of real-world problems by differential equations.