| The stability theory is a basic and important theory in differential equations and differential difference equations fields. In this paper, firstly, the author present some integral inequalities and discuss the stability, uniform stability and asymptotic stability of the differential equations by the integral inequality; secondly, the author generalize a differential-difference inequations and discuss the stability of some differential equations with time delay by the differential- difference inequations; finally, the author discuss the partial asymptotic stability of the differential equations.The whole paper consists three parts.Chapter 1: On some integral inequalities and its applications of the stability theory.Chapter 2: On differential-difference inequations and its applications.Chapter 3: On the partial asymptotic stability of the differential equations.
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