Boundary value problem for the second order impulsive delay differential equations

Skóra, Lidia

doi:10.1515/aupcsm-2015-0002

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“…The classic impulsive theory can be seen in [1,2]. In the last two decades, a vast literature on impulsive differential problems has been produced, such as [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], only to mention a few.…”

Section: Introductionmentioning

confidence: 99%

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

Minhós

Carapinha

2021

Journal of Function Spaces

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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.

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