Some Integral Inequalities with Maximum of the Unknown Functions

This paper deals with a special type of delayed integral inequalities of Bihary type for scalar functions of two variables. The integrals involve the maximum of the unknown function over a past time interval. Several nonlinear types of integral inequalities are solved. The importance of these integral inequalities is based on their wide applications to the qualitative investigations of various properties of solutions of partial differential equations with “maxima ” and it is illustrated by some direct applications