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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 Citation - Scopus: 2Lyapunov Type Inequalities for Second-Order Differential Equations With Mixed Nonlinearities(Walter de Gruyter GmbH, 2016) Agarwal,R.P.; Özbekler,A.In this paper,we present some new Lyapunov and Hartman type inequalities for second-order equations with mixed nonlinearities: x''(t) + p(t)|x(t)|β?1x(t) + q(t)|x(t)|y?1x(t) = 0, where p(t), q(t) are real-valued functions and 0 < γ < 1 < β < 2. No sign restrictions are imposed on the potential functions p(t) and q(t). The inequalities obtained generalize the existing results for the special cases of this equation in the literature. © 2016 by De Gruyter.
