Browsing by Author "Sirma, Ali"

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Adjoint Systems and Green Functionals for Second-Order Linear Integro-Differential Equations With Nonlocal Conditions
(Texas State Univ, 2015) Sirma, Ali
In this work, we generalize so called Green's functional concept in literature to second-order linear integro-differential equation with nonlocal conditions. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order integro-differential equation is reduced to one and one integral equation to identify the Green's solution. The coefficients of the equation are assumed to be generally nonsmooth functions satisfying some general properties such as p-integrability and boundedness. We obtain new adjoint system and Green's functional for second-order linear integro-differential equation with nonlocal conditions. An application illustrate the adjoint system and the Green's functional. Another application shows when the Green's functional does not exist.
Existence and Uniqueness of Periodic Solutions for a Kind of Rayleigh Equation With Finitely Many Deviating Arguments
(Pergamon-elsevier Science Ltd, 2010) Sirma, Ali; Tunc, Cemil; Ozlem, Semih
In this paper, we consider a kind of Rayleigh equation with finitely many deviating arguments of the form x '' + f(t, x'(t)) + Sigma(n)(k=1) g(k)(t, x(t - tau(k)(t))) = p(t). By using the coincidence degree theory, we establish the results on the existence and uniqueness of periodic solutions for the above equation. The results we obtained include and improve the results existing in the literature. (C) 2010 Elsevier Ltd. All rights reserved.
A Note on Coincidence Degree Theory
(Hindawi Ltd, 2012) Sirma, Ali; Sevgin, Sebaheddins
The background of definition of coincidence degree is explained, and some of its basic properties are given.
Stability Analysis of a Class of Generalized Neutral Equations
(Eudoxus Press, Llc, 2010) Tunc, Cemil; Sirma, Ali
In this paper, some sufficient conditions for all solutions of a class of generalized neutral equations to approach zero as t -> infinity are presented. Based on Lyapunov's functional approach, some new stability criteria are derived. Our results improve and include some related results existing in the literature.