• 제목/요약/키워드: neutral delay equation

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OSCILATION AND STABILITY OF NONLINEAR NEUTRAL IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

  • Duan, Yongrui;Tian, Peng;Zhang, Shunian
    • Journal of applied mathematics & informatics
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    • 제11권1_2호
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    • pp.243-253
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    • 2003
  • In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

Oscillatory Behavior of Linear Neutral Delay Dynamic Equations on Time Scales

  • Saker, Samir H.
    • Kyungpook Mathematical Journal
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    • 제47권2호
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    • pp.175-190
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    • 2007
  • By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation $$(y(t)+r(t)y({\tau}(t)))^{{\Delta}{\Delta}}+p(t)y(\delta(t))=0$$, on a time scale $\mathbb{T}$ are established. Our results as a special case when $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{N}$ improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when $\mathbb{T}=q^{\mathbb{N}}$, i.e., for second-order $q$-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.

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EXISTENCE AND CONTROLLABILITY OF IMPULSIVE FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH STATE DEPENDENT INFINITE DELAY VIA SECTORIAL OPERATOR

  • MALAR, K.;ILAVARASI, R.;CHALISHAJAR, D.N.
    • Journal of Applied and Pure Mathematics
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    • 제4권3_4호
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    • pp.151-184
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    • 2022
  • In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

SOLVABILITY OF IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS WITH STATE DEPENDENT DELAY

  • Karthikeyan, K.;Anguraj, A.
    • Journal of applied mathematics & informatics
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    • 제30권1_2호
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    • pp.57-69
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    • 2012
  • In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

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.

SOLVABILITY OF A THIRD ORDER NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION

  • Liu, Zeqing;Wang, Wei;Park, Jong Seo;Kang, Shin Min
    • 충청수학회지
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    • 제23권3호
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    • pp.443-452
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    • 2010
  • This work deals with the existence of uncountably many bounded positive solutions for the third order nonlinear neutral delay differential equation $$\frac{d^3}{dt^3}[x(t)+p(t)x(t-{\tau})]+f(t,x(t-{{\tau}_1}),{\ldots},x(t-{{\tau}_k}))=0,\;t{\geq}t_0$$ where ${\tau}>0$, ${\tau}_i{\in}{\mathbb{R}^+}$ for $i{\in}\{1,2,{\ldots},k\}$, $p{\in}C([t_0,+{\infty}),{\mathbb{R}^+})$ and $f{\in}C([t_0,+{\infty}){\times}{\mathbb{R}^k},{\mathbb{R}})$.

Oscillation and Nonoscillation of Nonlinear Neutral Delay Differential Equations with Several Positive and Negative Coefficients

  • Elabbasy, Elmetwally M.;Hassan, Taher S.;Saker, Samir H.
    • Kyungpook Mathematical Journal
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    • 제47권1호
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    • pp.1-20
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    • 2007
  • In this paper, oscillation and nonoscillation criteria are established for nonlinear neutral delay differential equations with several positive and negative coefficients $$[x(t)-R(t)x(t-r)]^{\prime}+\sum_{i=1}^{m}Pi(t)H_i(x(t-{\tau}_i))-\sum_{j=1}^{n}Q_j(t)H_j(x(t-{\sigma}_j))=0$$. Our criteria improve and extend many results known in the literature. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation with constant coefficients, $$y^{\prime}(t)+\sum_{i=1}^{m}(p_i-\sum_{k{\in}J_i}qk)y(t-{\tau}_i)=0$$, oscillates, then every solution of the nonlinear equation also oscillates.

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