On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications
During the past years, a number of efforts have been devoted to the integral inequalities. The results given by Gronwall, Bellman and Bihari and their linear and nonlinear generalizations in the case of continuous and discontinuous functions provide a fundamental role in the study of many qualitative properties of differential and integral equations (see [\textit{A. Gallo} and \textit{A. M. Piccirillo}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 5, 1550--1559 (2007; Zbl 1124.26013)]). The authors give explicit bounds to some new nonlinear integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions, which develop and improve certain results which were proved by \textit{F. Jiang} and \textit{F. Meng} [J. Comput. Appl. Math. 205, No. 1, 479--486 (2007; Zbl 1135.26015)]. An example is presented to show estimated solutions for an impulsive differential system. The article is systematically well-organized, and will be useful for beginners in the theory of integral inequalities.
scientific article; zbMATH DE number 6529292
scientific article