Generalization of Lemma Gronwall–Bellman on Retarded Integral Inequality

Abstract

On the basis of the integral inequalities in [9], this paper establish several general form Gronwall–Bellman nonlinear retarded integral inequalities, which contain multi-different power terms of unknown function inside integral sign. Using integral and differential skills, we obtain some new results which provide explicit bounds on unknown functions in the integral inequalities. The explicit bounds given here can be used as tools in the study of existence, uniqueness, boundedness, stability, invariant manifolds and other qualitative properties of solutions of differential equations and integral equation. An example is given to illustrate the effectiveness of our results in estimation of solutions of some differential equations.