A Class Of Nonlinear Integral Inequality And Its Application

Integral inequality plays an important role in the character of the solutionof diferential equations, diference equations, and other types of equations. Inthis paper, we major in Several types of integral inequality and obtain many newresults, based on the type of Pachpatte inequality and Bellman inequality. Thethesis is divided into four chapters.Chapter1, a class of new nonlinear retarded integral inequalities are estab-lished which extend several existing results, and are used to study the bounded-ness and asymptotic quality of the new type integral equations.Chapter2, we study some integral inequalities with one variable, thus obtainsome more wider results, which have provided a powerful tool for the study ofthe character of the diferential equations.Chapter3, based on chapter2, we study some new integral inequalities withtwo variable. The new results have popularized the existed ones.Chapter4, by using Gronwall inequality, we establish some new discontin-uous Gronwall-Bellman-Ou-Lang type inequality. The results can be used forretarded integral inequalitie and also widen corresponding centain continuousand discrete equalities.