Electron. J. Differential Equations, Vol. 2019 (2019), No. 46, pp. 1-14.

Quasilinearization method for first-order impulsive integro-differential equations

Peiguang Wang, Chongrui Li, Juan Zhang, Tongxing Li

Abstract:
In this article we study first-order impulsive integro-differential equations with integral boundary conditions, employing the method of quasilinearization with reversed ordering upper and lower solutions. We obtain two monotone sequences of iterates converging uniformly and quadratically to the unique solution of the problem. Two examples are given to illustrate the applications of the established results.

Submitted February 26, 2018. Published March 30, 2019.
Math Subject Classifications: 34D20, 34A37.
Key Words: Impulsive integro-differential equations; quasilinearization; integral boundary conditions; quadratic convergence; upper and lower solutions.

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Peiguang Wang
College of Mathematics and Information Science
Hebei University
Baoding, Hebei 071002, China
email: pgwang@hbu.edu.cn
Chongrui Li
College of Mathematics and Information Science
Hebei University
Baoding, Hebei 071002, China
email: 1065265114@qq.com
Juan Zhang
College of Mathematics and Information Science
Hebei University
Baoding, Hebei 071002, China
email: smaths@hbu.edu.cn
Tongxing Li
School of Information Science and Engineering
Linyi University
Linyi, Shandong 276005, China
email: litongx2007@163.com

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