Displaying similar documents to “Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces”

Maximal regularity of second-order evolution equations with infinite delay in Banach spaces

Xianlong Fu, Ming Li (2014)

Studia Mathematica

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By using Fourier multiplier theorems we characterize the existence and uniqueness of periodic solutions for a class of second-order differential equations with infinite delay. We also establish maximal regularity results for the equations in various spaces. An example is provided to illustrate the applications of the results obtained.

Maximal regularity of delay equations in Banach spaces

Carlos Lizama, Verónica Poblete (2006)

Studia Mathematica

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We characterize existence and uniqueness of solutions for an inhomogeneous abstract delay equation in Hölder spaces. The main tool is the theory of operator-valued Fourier multipliers.

Existence results for delay second order differential inclusions

Dalila Azzam-Laouir, Tahar Haddad (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.

On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

Ch. G. Philos (2007)

Annales Polonici Mathematici

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This article is concerned with a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems. By the use of the Schauder-Tikhonov theorem, a result on the existence of solutions is obtained. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of solutions is established. Moreover, these results are applied to the special case of ordinary differential systems and to a certain class of delay differential...

Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil Kpoumiè, Khalil Ezzinbi, David Békollè (2017)

Nonautonomous Dynamical Systems

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The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring...

Global existence and energy decay of solutions to a Bresse system with delay terms

Abbes Benaissa, Mostefa Miloudi, Mokhtar Mokhtari (2015)

Commentationes Mathematicae Universitatis Carolinae

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We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.

Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

Periodic solutions for some delay differential equations appearing in models of power systems

Bingwen Liu, Lihong Huang (2005)

Annales Polonici Mathematici

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The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.