Advances in Opial's type integral inequalities

Abstract

Opial's inequality and its generalizations, extensions and discretizations play a fundamental role in the study of existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations. Over the years, Opial's type integral inequalities have been receiving non-diminishing attention. In this article, we establish some new Opial's type integral inequalities which in special cases yield some existing results of Rozanova, Agarwal-Pang, Pachpatte, Das and Agarwal-Sheng, and provide new and handy tools to qualitative as well as quantitative analysis of solutions to differential equations.