Periodic boundary value problems for second-order impulsive integro-differential equations

Abstract

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second-order nonlinear impulsive integro-differential equations of mixed type.

Periodic boundary value problems of second-order impulsive differential equations

“…Second-order impulsive differential equations have been discussed by Ding et al [8,9], Chen et al [6], Jankowski [14] and Yang and Shen [25]. But in these papers, it is assumed that ∆x(t k ) = L k x (t k ), ∆x (t k ) = I k (x(t k )) and f is independent of x (t).…”

Periodic and homoclinic solutions generated by impulses

“…Such processes naturally occur in control theory, biology, optimization theory and some physics and mechanics problems. Due to their significance, a lot of efforts have been made in studying the qualitative properties of such systems; see, for instance, [1][2][3][4][5][6][7][8][9][10][11].…”

New algorithm for second-order boundary value problems of integro-differential equation

“…There has been a great deal of research work [1][2][3] on the existence of solutions for boundary value problems. However, very few attempts have been made to investigate boundary value problems in reproducing kernel spaces.…”