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Öğe Asymptotic properties of solutions of third-order nonlinear neutral dynamic equations(SPRINGER INTERNATIONAL PUBLISHING AG, 2014) Candan, TuncayThe purpose of this article is to give oscillation criteria for the third-order neutral dynamic equation (r(2)(t)[(r(1)(t)[y(t) + p(t)y(tau (t))](Delta))(Delta)](gamma))(Delta) + f (t, y(delta(t))) = 0, where gamma >= 1 is a ratio of odd positive integers with r(1)(t), r(2)(t), and p(t) are positive real-valued rd-continuous functions defined on T. We give new results for the third-order neutral dynamic equations and an example to illustrate the importance of our results.Öğe EXISTENCE OF NON-OSCILLATORY SOLUTIONS TO FIRST-ORDER NEUTRAL DIFFERENTIAL EQUATIONS(TEXAS STATE UNIV, 2016) Candan, TuncayThis article presents sufficient conditions for the existence of non oscillatory solutions to first-order differential equations having both delay and advance terms, known as mixed equations. Our main tool is the Banach contraction principle.Öğe Existence of non-oscillatory solutions to first-order neutral differential equations(Texas State University - San Marcos, 2016) Candan, TuncayThis article presents sufficient conditions for the existence of nonoscillatory solutions to first-order differential equations having both delay and advance terms, known as mixed equations. Our main tool is the Banach contraction principle. © 2016 Texas State University.Öğe Existence of positive periodic solutions of first-order neutral differential equations(WILEY-BLACKWELL, 2017) Candan, TuncayThis paper presents the existence of positive periodic solutions for first-order neutral differential equation with distributed deviating arguments. We apply Krasnoselskii's fixed point theorem to obtain our results. An example is given to support the theory. Copyright (C) 2016 John Wiley & Sons, Ltd.Öğe Existence of positive solutions of higher-order nonlinear neutral equations(SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Candan, TuncayIn this work, we consider the existence of positive solutions of higher-order nonlinear neutral differential equations. In the special case, our results include some well-known results. In order to obtain new sufficient conditions for the existence of a positive solution, we use Schauder's fixed point theorem.Öğe Oscillation criteria for second-order nonlinear neutral dynamic equations with distributed deviating arguments on time scales(SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Candan, TuncayIn this article, we establish some new oscillation criteria and give sufficient conditions to ensure that all solutions of nonlinear neutral dynamic equation of the form (r(t)((y(t) + p(t)y(tau(t)))(Delta))(gamma))(Delta) + integral(b)(a)f(t,y(delta(t,xi)))Delta xi = 0 are oscillatory on a time scale , where is a quotient of odd positive integers.Öğe OSCILLATION OF SOLUTIONS FOR ODD-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS(TEXAS STATE UNIV, 2010) Candan, TuncayIn this article, we establish oscillation criteria for all solutions to the neutral differential equations [x(t) +/- ax(t +/- h) +/- bx(t +/- g)]((n)) = p integral(d)(c) x(t - xi)d xi + q integral(d)(c) x(t + xi) d xi, where n is odd, h, g, a and b are nonnegative constants. We consider 10 of the 16 possible combinations of +/- signs, and give some examples to illustrate our results.Öğe Qualitative Theory of Differential, Difference, and Dynamic Equations(Hindawi Ltd, 2014) Li, Tongxing; Candan, Tuncay; Thandapani, Ethiraju[Abstract Not Available]
