Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations

Ravi P. Agarwal and Abdullah Özbekler

Applied Mathematics and Computation, 2016, vol. 282, issue C, 216-225

Abstract: In 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)|x(t)|β−1x(t)+q(t)|x(t)|γ−1x(t)=f(t),t≠θi;Δx′(t)+pi|x(t)|β−1x(t)+qi|x(t)|γ−1x(t)=fi,t=θi,where p, q, f are real-valued functions, {pi}, {qi}, {fi} are real sequences and 0 < γ < 1 < β < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {pi}, {qi}, {fi}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature.

Keywords: Lyapunov type inequality; Mixed nonlinear; Sub-linear; Super-linear; Forced; Impulse (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:282:y:2016:i:c:p:216-225

DOI: 10.1016/j.amc.2016.02.015

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