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Article Citation - WoS: 9Citation - Scopus: 10Lyapunov Type Inequalities for Nth Order Forced Differential Equations With Mixed Nonlinearities(Amer inst Mathematical Sciences-aims, 2016) Agarwal, Ravi P.; Ozbekler, AbdullahIn the case of oscillatory potentials, we present Lyapunov type inequalities for nth order forced differential equations of the form x((n))(t) + Sigma(m)(j=1) qj (t)vertical bar x(t)vertical bar(alpha j-1)x(t)= f(t) satisfying the boundary conditions x(a(i)) = x(1)(a(i)) = x(11)(ai) = center dot center dot center dot = x((ki))(ai) = 0; i = 1, 2,..., r, where a(1) < a(2) < ... < a(r), 0 <= k(i) and Sigma(r)(j=1) k(j) + r = n: r >= 2. No sign restriction is imposed on the forcing term and the nonlinearities satisfy 0 < alpha(l) < ... < alpha a(j) < 1 < alpha a(j+1) < ... < alpha(m) < 2. The obtained inequalities generalize and compliment the existing results in the literature.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 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.
