The Generalized Quasi-linearization Method Of Volterra-type Impulsive Equations In Banach Space

The impulsive integro-differential equations of two Volterra types in Banach space are discussed by means of generalized quasi-linearized method in this thesis. The thesis mainly focuses on two aspects:one is related to the discussion of the first order impulsive integro-differential equation in Banach space by means of generalized quasi-linearization method; the other one is concerned about the discussion of the second order impulsive integro-differential equations in Banach space by means of generalized quasi-linearization method.First of all, the thesis generalizes the main work by giving a summary and review about the historical background and development. Secondly, the author discusses the solution of the first order impulsive differential inequality by employing the method of generalized quasi-linearization in Banach space, gives the iterative sequence of the solution, and testifies the result of squaring converge to the solution; Finally the thesis discusses the second order impulsive equations. In the process of talking about the second order equation, the thesis uses impulsive differential inequality twice which leads to the conclusion in the end.