Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 46, pp. 1-14.

Title: Quasilinearization method for first-order impulsive integro-differential equations

Authors: Peiguang Wang (Hebei Univ., Baoding, Hebei, China)
         Chongrui Li   (Hebei Univ., Baoding, Hebei, China)
         Juan Zhang    (Hebei Univ., Baoding, Hebei, China)
         Tongxing Li   (Hebei Univ., Baoding, Hebei, China)
 
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: mpulsive integro-differential equations; quasilinearization;
           integral boundary conditions; quadratic convergence; upper and lower solutions.