Lyapunov type inequalities for second-order differential equations with mixed nonlinearities

Abstract

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.