Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

Using the Monch fixed point theorem and progressive estimation method,we study the existence,uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces.The compactness assumption on associated family of operators and the impulsive term,some restrictive conditions on a priori estimation,noncompactness measure estimation and the impulsive term have not been used,our results are different from some known results.Finally,a noncompact semigroup example explains the obtained results.