A note on the qualitative behaviors of non-linear Volterra integro-differential equation
(2016). A note on the qualitative behaviors of non-linear Volterra integro-differential equation. EKB Journal Management System, 24(2), 187-192. doi: 10.1016/j.joems.2014.12.010
. "A note on the qualitative behaviors of non-linear Volterra integro-differential equation". EKB Journal Management System, 24, 2, 2016, 187-192. doi: 10.1016/j.joems.2014.12.010
(2016). 'A note on the qualitative behaviors of non-linear Volterra integro-differential equation', EKB Journal Management System, 24(2), pp. 187-192. doi: 10.1016/j.joems.2014.12.010
A note on the qualitative behaviors of non-linear Volterra integro-differential equation. EKB Journal Management System, 2016; 24(2): 187-192. doi: 10.1016/j.joems.2014.12.010

A note on the qualitative behaviors of non-linear Volterra integro-differential equation

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2, 2016, Pages 187-192    PDF (352.1 K)
DOI: 10.1016/j.joems.2014.12.010
Abstract
This paper considers a scalar non-linear Volterra integro-differential equation. We
establish sufficient conditions which guarantee that the solutions of the equation are stable, globally
asymptotically stable, uniformly continuous on [0 , ∞ ) , and belongs to L 1 [0 , ∞ ) and L 2 [0 , ∞ )
and have bounded derivatives. We use the Lyapunov’s direct method to prove the main results.
Examples are also given to illustrate the importance of our results. The results of this paper are new
and complement previously known results
Keywords
Volterra integro-differential equation; Riemann integrable; Bounded derivatives; Lyapunov functional
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