On nonlinear impulsive differential systems with canonical and non-canonical operators

Abstract

The investigation on the oscillatory and asymptotic properties of differential equations plays an important role in many applications, such as engineering, physics and medicine. In this work, we establish some new sufficient conditions for both the oscillatory and asymptotic behavior of the solutions to a second-order neutral impulsive differential system (IDS, for short) with deviating argument and fixed moments of impulse effect under both canonical and non-canonical operators with various values of the neutral coefficient. Also, we obtain the condition for the existence of a positive solution of the system under consideration. Finally, two examples are provided to illustrate the main results.

Keywords:

• Impulses
• neutral differential equations
• nonlinear equations
• oscillation
• asymptotic behavior

2010 Mathematics Subject Classifications:

• 34A37
• 34K11

Acknowledgements

Marianna Ruggieri is a member of the INdAM (Istituto Nazionale di Alta Matematica “Francesco Severi”) Research group GNFM (Gruppo Nazionale per la Fisica Matematica). Andrea Scapellato is a member of the INdAM (Istituto Nazionale di Alta Matematica “Francesco Severi”) Research group GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni). All the authors contributed equally to this work. The authors are listed in alphabetical order.

Disclosure statement

No potential conflict of interest was reported by the authors.