Abstract
In this paper, the Mönch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Guo Dajun, Nonlinear impulsive Volterra integral equations in Banach spaces and applications, J. Appl. Math. Stochastic Anal., 1993, 6: 35–48.
Guo Dajun and Lakshmikantham, V., Nonlinear Problems in Abstract Cones, Academic Press, Inc., Boston and New York, 1988.
Guo Dajun, Impulsive integral equations in Banach spaces and applications, J. Appl. Math. Stochastic Anal., 1992, 5: 111–122.
Heinz, H. P., On the behavior of measure of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal., 1983, 7: 1352–1371.
Mönch, H., Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. TMA, 1980, 4: 985–999.
Liu Lishan, Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces, India J. Pure Appl. Math., 1996, 27: 959–972.
Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of Impulsive Differential Equations, World Sci. Publishing Co., Inc., Singapore, 1989.
Author information
Authors and Affiliations
Additional information
Project Supported by National Natural Science Foundation of China (19871048) and Natural Science Foundation of Shandong Province of China (Y98A09012).
Rights and permissions
About this article
Cite this article
Rengui, L., Changyin, D. Existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces. Appl. Math. Chin. Univ. 15, 281–288 (2000). https://doi.org/10.1007/s11766-000-0052-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11766-000-0052-1