Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces

Authors:
Xinguang Zhang;Lishan Liu
Affiliations:
Department of Mathematics, Qufu Normal University, Qufu, Shandong, People's Republic of China;Department of Mathematics, Qufu Normal University, Qufu, Shandong, People's Republic of China
Venue:
Nonlinear Analysis: Theory, Methods & Applications
Year:
2006

Citing 1
Cited 2

Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications

Global solutions for second order impulsive integro-differential equations in Banach spaces

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The solutions of initial value problems for nonlinear fourth-order impulsive integro-differential equations in banach spaces

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Abstract

In this paper, through solving equations step by step, without any assumption of compactness-type conditions, we obtain unique solution of initial value problems of nonlinear second order impulsive integral-differential in Banach spaces. The results obtained generalize and improve the corresponding results of Guo and Chai in papers [D.J. Guo, Initial value problems for nonlinear second-order impulsive integro-differential equations in Banach spaces, J. Math. Anal. Appl. 200 (1996) 1-13; G.Q. Chai, Initial value problems for nonlinear second order impulsive integro-differential equations in Banach space, Acta Math. Sinica 20 (3) (2000) 351-359 (in Chinese)].