Mouffak Benchohra, Imene Medjadj (2016)
Commentationes Mathematicae Universitatis Carolinae
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Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.
Sokhadze, Z. (1995)
Memoirs on Differential Equations and Mathematical Physics
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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.
Abdessalam Baliki, Mouffak Benchohra (2014)
Nonautonomous Dynamical Systems
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In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
Tran Dinh Ke, Valeri Obukhovskii, Ngai-Ching Wong, Jen-Chih Yao (2011)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given. ...
Miao Li, Xiao-Hui Gu, Fa-Lun Huang (2004)
Studia Mathematica
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Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.
Nagel, Rainer, Nguyen Thieu Huy (2003)
International Journal of Mathematics and Mathematical Sciences
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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.
Diekmann, Odo
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Lamine Bouzettouta, Sabah Baibeche, Manel Abdelli, Amar Guesmia (2023)
Mathematica Bohemica
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The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first...