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

作　　者：Sheng-li XIE Yi-ming XIE 

机构地区：[1]School of Mathematics&Physics,Urban Construction College,Anhui Jianzhu University [2]School of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China

出　　处：《Acta Mathematicae Applicatae Sinica》2019年第3期564-579,共16页应用数学学报（英文版）

基　　金：Supported in part by the Natural Science Foundation of Anhui Province(11040606M01);Anhui Educational Committee(KJ2012A055),China

摘　　要：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.Using the M¨onch 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.

关 键 词：DAMPED second order IMPULSIVE functional differential equations MILD SOLUTION strong SOLUTION classical SOLUTION measure of noncompactness 

分 类 号：O1[理学—数学]