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

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  • Agarwal, Ravi P.
  • Özbekler, Abdullah

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.

Suggested Citation

  • Agarwal, Ravi P. & Özbekler, Abdullah, 2016. "Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 216-225.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:216-225
    DOI: 10.1016/j.amc.2016.02.015
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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    3. Agarwal, Ravi P. & Özbekler, Abdullah, 2015. "Disconjugacy via Lyapunov and Vallée-Poussin type inequalities for forced differential equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 456-468.
    4. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Dynamic complexity of a two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 131-139.
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