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

Cemil Tunç | Zendy

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

Author(s) -

Cemil Tunç

Publication year - 2015

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 , volterra equations , scalar (mathematics) , integro differential equation , differential equation , bounded function , volterra integral equation , complement (music) , nonlinear system , mathematical analysis , 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

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