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

摘要

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-1)x(t) + q(t)|x(t)|~(γ-1)x(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.