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Article Citation - WoS: 3Citation - Scopus: 3Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, AbdullahIn this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.Article Citation - WoS: 19Citation - Scopus: 21Lyapunov Type Inequalities for Mixed Nonlinear Riemann-Liouville Fractional Differential Equations With a Forcing Term(Elsevier, 2017) Agarwal, Ravi P.; Ozbekler, AbdullahIn this paper, we present some new Lyapunov and Hartman type inequalities for Riemann-Liouville fractional differential equations of the form ((a)D(alpha)x)(t) + p(t) vertical bar x(t) vertical bar(mu-1) x(t) + q(t) vertical bar x(t) vertical bar(gamma-1) x(t) = f(t), where p, q, f are real-valued functions and 0 < gamma < 1 < mu < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier B.V. All rights reserved.Review Citation - WoS: 3Citation - Scopus: 3Lyapunov Type Inequalities for Second Order Forced Mixed Nonlinear Impulsive Differential Equations(Elsevier Science inc, 2016) Agarwal, Ravi P.; Ozbekler, AbdullahIn this paper, we present some new Lyapunov and Hartman type inequalities for second order forced impulsive differential equations with mixed nonlinearities: x ''(t) + p(t)vertical bar x(t)vertical bar(beta-1)x(t) + q(t)vertical bar x(t)vertical bar(gamma-1)x(t) = f(t), t not equal theta(i); Delta x'(t) + p(i)vertical bar x(t)vertical bar(beta-1)x(t) + q(i)vertical bar x(t)vertical bar(gamma-1) x(t) = f(i), t = theta(i), where p, q, f are real-valued functions, {p(i)}, {q(i)}, {f(i)} are real sequences and 0 < gamma < 1 < beta < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {p(i)}, {q(i)}, {f(i)}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier Inc. All rights reserved.
