Integral inequalities similar to Gronwall inequality

Abstract

In the present paper, we establish some nonlinear integral inequalities for functions of one variable, with a further generalization functions with n independent variables. We apply our results to a system of nonlinear differential equations for functions of one variable and to the nonlinear hyperbolic partial integrodifferential equation in n-independent variables. These results extend the Gronwall type inequalities obtained by Pachpatte [6] and Oguntuase [5].