Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses

By Malik Muslim, Avadhesh Kumar, Michal Feckan. 2016

73 citations recorded by the source corpus.

Abstract In this paper, we consider a non-instantaneous impulsive system represented by second order nonlinear differential equation with deviated argument in a Banach space X . We used the strongly continuous cosine family of linear operators and Banach fixed point method to study the existence and uniqueness of the solution of the non-instantaneous impulsive system. Also, we study the existence and uniqueness of the solution of the nonlocal problem and stability of the non-instantaneous impulsive system. Finally, we give examples to illustrate the application of these abstract results.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/84ce39e54394cbe3a92243afe1058cf2e1f9dbe3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Rajesh Dhayal
2. Muslim Malik
3. Syed Abbas

In Modeling and Simulation

1. Rajesh Dhayal
2. Muslim Malik
3. Syed Abbas

Citations in the corpus

• Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps (2020, background): “For more details on non-instantaneous impulses, one can see [13-17] and the references cited therein.”