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Article Forced Oscillation of Delay Difference Equations Via Nonprincipal Solution(Wiley, 2018) Ozbekler, AbdullahIn this paper, we obtain a new oscillation result for delay difference equations of the form Delta(r(n)Delta x(n)) + a(n)x(tau n) = b(n); n is an element of N under the assumption that corresponding homogenous equation Delta(r(n)Delta z(n)) + a(n)z(n+1) = 0; n is an element of N is nonoscillatory, where tau(n) <= n + 1. It is observed that the oscillation behaviormay be altered due to presence of the delay. Extensions to forced Emden-Fowler-type delay difference equations Delta(r(n)Delta x(n)) + a(n)vertical bar x(tau n)vertical bar(alpha-1)x(tau n) = b(n); n is an element of N in the sublinear (0 < alpha < 1) and the superlinear (1 < alpha) cases are also discussed.Article Citation - WoS: 1Citation - Scopus: 1Sturmian Comparison Theory for Half-Linear and Nonlinear Differential Equations Via Picone Identity(Wiley, 2017) Ozbekler, AbdullahIn this paper, Sturmian comparison theory is developed for the pair of second-order differential equations; first of which is the nonlinear differential equations of the form (m(t) Phi(beta)(y'))' + Sigma(n)(i=1) q(i)(t) Phi(alpha i)(y) = 0 and the second is the half-linear differential equations (k(t)Phi(beta)(x'))' + p(t)Phi(beta)(x) = 0 where Phi(alpha)(s) = vertical bar s vertical bar(alpha-1)s and alpha(1) > ... > alpha(m) > beta > alpha(m+1) > ... > alpha(n) > 0. Under the assumption that the solution of has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for (1). Examples are given to illustrate the relevance of the results. Copyright (c) 2016 John Wiley & Sons, Ltd.Article On the Oscillation of Discrete Volterra Equations With Positive and Negative Nonlinearities(Rocky Mt Math Consortium, 2018) Ozbekler, AbdullahIn this paper, we give new oscillation criteria for discrete Volterra equations having different nonlinearities such as super-linear and sub-linear cases. We also present some new sufficient conditions for oscillation under the effect of the oscillatory forcing term.Article Sturmian Comparison Theory for Half-Linear and Nonlinear Differential Equations Via Picone Identity(Univ Nis, Fac Sci Math, 2017) Ozbekler, AbdullahIn this paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations of the form (m(t)Phi(beta) (y'))' + Sigma (n) (i = 1) qi(t)Phi(alpha i) (y) = 0 and the second is the half-linear differential equations (k(t)Phi(beta) (x'))' + p(t) Phi(beta) (x) = 0 where Phi(*)(s) = \ s \(*-1)s and alpha(1) > . . .> alpha(m) > beta > alpha(m + 1) > . . . > alpha(n) > 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results.Article Citation - Scopus: 1On the Oscillation of Volterra Integral Equations With Positive and Negative Nonlinearities(Wiley-blackwell, 2016) Ozbekler, AbdullahIn the paper, we give new oscillation criteria for Volterra integral equations having different nonlinearities such as superlinearity and sublinearity. We also present some new sufficient conditions for oscillation under the effect of oscillatory forcing term. Copyright (C) 2015 JohnWiley & Sons, Ltd.
