• 제목/요약/키워드: nonlinear delay difference equations

검색결과 7건 처리시간 0.023초

STABILITY IN FUNCTIONAL DIFFERENCE EQUATIONS WITH APPLICATIONS TO INFINITE DELAY VOLTERRA DIFFERENCE EQUATIONS

  • Raffoul, Youssef N.
    • 대한수학회보
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    • 제55권6호
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    • pp.1921-1930
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    • 2018
  • We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

ON THE OSCILLATION OF SECOND-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

  • Zhang, Quanxin;Sogn, Xia;Gao, Li
    • Journal of applied mathematics & informatics
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    • 제30권1_2호
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    • pp.219-234
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    • 2012
  • By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criterion for the second-order nonlinear delay dynamic equations $$(a(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+q(t)f(x({\tau}(t)))=0$$ on a time scale $\mathbb{T}$, here ${\gamma}{\geq}1$ is the ratio of two positive odd integers with $a$ and $q$ real-valued positive right-dense continuous functions defined on $\mathbb{T}$. Our results not only extend and improve some known results, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

OSCILLATION OF NONLINEAR SECOND ORDER NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES

  • Agwo, Hassan A.
    • 대한수학회보
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    • 제45권2호
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    • pp.299-312
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    • 2008
  • In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

CLASSIFICATION AND EXISTENCE OF NONOSCILLATORY SOLUTIONS OF HIGHER ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS

  • ZHOU YONG;LI C. F.
    • Journal of applied mathematics & informatics
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    • 제18권1_2호
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    • pp.127-144
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    • 2005
  • In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY

  • MAROUN MARIETTE R.;RAFFOUL YOUSSEF N.
    • 대한수학회지
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    • 제42권2호
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    • pp.255-268
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    • 2005
  • We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.