• Title/Summary/Keyword: infinite delay

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CONTROLLABILITY OF IMPULSIVE FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY IN BANACH SPACES

  • Chang, Yong-Kui
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.137-154
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    • 2007
  • In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

COMPLETE CONTROLLABILITY OF SEMILINEAR STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH INFINITE DELAY AND POISSON JUMPS

  • D.N., CHALISHAJAR;A., ANGURAJ;K., RAVIKUMAR;K., MALAR
    • Journal of Applied and Pure Mathematics
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    • v.4 no.5_6
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    • pp.299-315
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    • 2022
  • This manuscript deals with the exact (complete) controllability of semilinear stochastic differential equations with infinite delay and Poisson jumps utilizing some basic and readily verified conditions. The results are obtained by using fixed-point approach and by using advance phase space definition for infinite delay part. We have used the axiomatic definition of the phase space in terms of stochastic process to consider the time delay of the system. An infinite delay along with the Poisson jump is the new investigation for the given stochastic system. An example is given to illustrate the effectiveness of the results.

BS-STABILITIES AND $\rho$-STABILITIES FOR FUNCTIONAL DIFFERENCE EQUATIONS WITH INFINITE DELAY

  • Choi, Sung Kyu;Goo, Yoon Hoe;Im, Dong Man;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.4
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    • pp.753-762
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    • 2012
  • We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

EXISTENCE RESULTS FOR NEUTRAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN BANACH SPACES

  • Chandrasekaran, S.;Karunanithi, S.
    • Journal of applied mathematics & informatics
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    • v.33 no.1_2
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    • pp.45-60
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    • 2015
  • This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

RANDOM ATTRACTOR FOR STOCHASTIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

  • You, Honglian;Yuan, Rong
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1469-1484
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    • 2014
  • In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

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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    • v.4 no.3_4
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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.

INFINITE HORIZON OPTIMAL CONTROL PROBLEMS OF BACKWARD STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Liang, Hong;Zhou, Jianjun
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.311-330
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    • 2020
  • This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

ADMISSIBLE INERTIAL MANIFOLDS FOR INFINITE DELAY EVOLUTION EQUATIONS

  • Minh, Le Anh
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.669-688
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    • 2021
  • The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

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

  • Raffoul, Youssef N.
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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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.