Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model

Abstract

In this paper, we consider a first-order coupled impulsive system of equations with functional boundary conditions, subject to the generalized impulsive effects. It is pointed out that this problem generalizes the classical boundary assumptions, allowing two-point or multipoint conditions, nonlocal and integrodifferential ones, or global arguments, as maxima or minima, among others. Our method is based on lower and upper solution technique together with the fixed point theory. The main theorem is applied to a SIRS model where to the best of our knowledge, for the first time, it includes impulsive effects combined with global, local, and the asymptotic behavior of the unknown functions.

First-order periodic coupled systems with generalized impulse conditions

“…Furthermore, results on equi-regulated functions are essential to deal with the discontinuities at the instants of impulse. A similar problem is studied in [19,20,21], and with similar techniques in [18,22].…”