On some new integral inequalities of Growall–Bellman type

摘要

In this paper, we establish some new integral inequalities of the Gronwall–Bellman type that have a wide range of the applications in the theory of ordinary differential equations. The purpose of this paper is to extend the results proved in G.B. Pachpatte [J. Math. Phys. Sci. 8 (1974) 309–318; Bull. Soc. Grece 15 (1974) 7–12; J. Math. Phys. Sci. 9 (1975) 405–416; J. Math. An a. Appl. 49 (1975) 794–802; 5 (1975) 141–150; 189 (1995) 128–144; 69 (1965) 362–367], for the continuous inequalities of Gronwall–Bellman and Reid type.