On a class of functional differential equations having slowly varying solutions.
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Takaŝi, Kusano, Marić, Vojislav (2006)
Publications de l'Institut Mathématique. Nouvelle Série
Adam Bobrowski, Małgorzata Kubalińska (2006)
Annales Polonici Mathematici
We study existence, uniqueness and form of solutions to the equation where α, β, γ and f are given, and stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.
Oplustil, Z., Sremr, J. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Qing-Long Han (2001)
International Journal of Applied Mathematics and Computer Science
This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.
Sergey Labovskiy, Mário Frengue Getimane (2014)
Mathematica Bohemica
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
Kvinikadze, G. (1999)
Memoirs on Differential Equations and Mathematical Physics
Lomtatidze, Alexander, Opluštil, Zdeněk (2003)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Philos, Christos G., Purnaras, Ioannis K. (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Pylypenko, Vita, Rontó, András (2008)
Journal of Inequalities and Applications [electronic only]
Eugene Bravyi (2011)
Mathematica Bohemica
Consider boundary value problems for a functional differential equation where are positive linear operators; is a linear bounded vector-functional, , , . Let the solvability set be the set of all points such that for all operators , with the problems have a unique solution for every and . A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl,...
Diblík, J., Zafer, A. (2011)
Abstract and Applied Analysis
Leonid Berezansky, Elena Braverman (2019)
Czechoslovak Mathematical Journal
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays where and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
Jan Čermák (1999)
Annales Polonici Mathematici
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.
Alexander Domoshnitsky, Robert Hakl, Bedřich Půža (2012)
Czechoslovak Mathematical Journal
Consider the homogeneous equation where is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
Raúl Naulin (2003)
Czechoslovak Mathematical Journal
The unstable properties of the linear nonautonomous delay system , with nonconstant delay , are studied. It is assumed that the linear system is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function and the results depending on the asymptotic properties of the...
Domoshnitsky, Alexander, Koplatadze, Roman (2007)
Journal of Inequalities and Applications [electronic only]
De La Sen, M., Jugo, J. (2004)
Journal of Applied Mathematics
Malkhaz Ashordia (2021)
Mathematica Bohemica
We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general...
Nguyen, Thanh Lan (2001)
Abstract and Applied Analysis
Malkhaz Ashordia (2016)
Mathematica Bohemica
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered....
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