Open AccessA note on the qualitative behaviors of non-linear Volterra integro-differential equation
Author(s) -
Cemil Tunç
Publication year - 2016
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2014.12.010
Subject(s) - mathematics , scalar (mathematics) , volterra equations , bounded function , complement (music) , differential equation , volterra integral equation , integro differential equation , mathematical analysis , nonlinear system , integral equation , first order partial differential equation , biochemistry , chemistry , physics , geometry , quantum mechanics , complementation , gene , phenotype
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 L1[0, ∞) and L2[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