A note on the qualitative behaviors of non-linear Volterra integro-differential equation | ||||
Journal of the Egyptian Mathematical Society | ||||
Volume 24, Issue 2, 2016, Page 187-192 PDF (352.1 K) | ||||
DOI: 10.1016/j.joems.2014.12.010 | ||||
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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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