The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations. (English) Zbl 0780.34006

Liz, E.; Nieto, Juan J.

Commentat. Math. Univ. Carol. 34, No. 3, 405-411 (1993).

Summary: We develop the monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for “impulsive functions” and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.

MSC:

34A37	Ordinary differential equations with impulses
34C25	Periodic solutions to ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34A45	Theoretical approximation of solutions to ordinary differential equations

Keywords:

monotone iterative technique; extremal solutions; second order periodic boundary value problem; impulsive effects; maximum principle