• Title, Summary, Keyword: neutral differential equations

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HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Dhage, Bapurao C.
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.315-330
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    • 2007
  • In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

AN EXISTENCE OF THE SOLUTION TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS UNDER SPECIAL CONDITIONS

  • KIM, YOUNG-HO
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.53-63
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    • 2019
  • In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

EXISTENCE AND REGULARITY FOR SEMILINEAR NEUTRAL DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Jeong, Jin-Mun
    • East Asian mathematical journal
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    • v.30 no.5
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    • pp.631-637
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    • 2014
  • In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS OF FIRST-ORDER NEUTRAL DIFFERENTIAL EQUATIONS

  • Rezaiguia, Ali;Ardjouni, Abdelouaheb;Djoudi, Ahcene
    • Honam Mathematical Journal
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    • v.40 no.1
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    • pp.1-11
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    • 2018
  • We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].

STABILITY IN NONLINEAR NEUTRAL LEVIN-NOHEL INTEGRO-DIFFERENTIAL EQUATIONS

  • Khelil, Kamel Ali;Ardjouni, Abdelouaheb;Djoudi, Ahcene
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.303-321
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    • 2017
  • In this paper we use the Krasnoselskii-Burton's fixed point theorem to obtain asymptotic stability and stability results about the zero solution for the following nonlinear neutral Levin-Nohel integro-differential equation $$x^{\prime}(t)+{\displaystyle\smashmargin{2}{\int\nolimits_{t-{\tau}(t)}}^t}a(t,s)g(x(s))ds+c(t)x^{\prime}(t-{\tau}(t))=0$$. The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi [20].

EXISTENCE OF THREE POSITIVE PERIODIC SOLUTIONS OF NEUTRAL IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Liu, Yuji;Xia, Jianye
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.243-256
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    • 2010
  • This paper is concerned with the neutral impulsive functional differential equations $$\{{x'(t)\;+\;a(t)x(t)\;=\;f(t,\;x(t\;-\;\tau(t),\;x'(t\;-\;\delta(t))),\;a.e.\;t\;{\in}\;R, \atop {\Delta}x(t_k)\;=\;b_kx(t_k),\;k\;{\in}\;Z.$$ Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.

Necessary and Sufficient Condition for the Solutions of First-Order Neutral Differential Equations to be Oscillatory or Tend to Zero

  • Santra, Shyam Sundar
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.73-82
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    • 2019
  • In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

EXISTENCE, UNIQUENESS AND STABILITY OF IMPULSIVE STOCHASTIC PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

  • Anguraj, A.;Vinodkumar, A.
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.739-751
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    • 2010
  • This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.