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On Asymptotically Autonomous Retarded Functional Differential Equations
2001
Journal of Mathematical Analysis and Applications
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The aim of the present paper is to investigate the asymptotic behavior of the solutions of the asymptotically autonomous retarded functional differential equa-Ž . Ž . tion x t s Lx q M t x . ...
Moreover, we give bounds on the rate of converp gence as well. ...
Consider a linear autonomous retarded functional differential equation Ž . ...
doi:10.1006/jmaa.2000.7221
fatcat:q25xz2ipbvg2vbp4uwsw4d6qje
On asymptotically autonomous differential equations in the plane
1997
Topological Methods in Nonlinear Analysis
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On Markus' theorem Our next theorem is concerned with one of the most important properties of asymptotically autonomous differential equations in the plane, presented by Markus in [10] . ...
The present paper is based on previous studies by Filippov on autonomous and perturbed autonomous differential equations, in particular, on planar ones, in the framework of the axiomatic theory. ...
doi:10.12775/tmna.1997.035
fatcat:iqfncs2zyfed3ovab75w3bl64y
Convergence to a steady state for asymptotically autonomous semilinear heat equations on RN
2011
Journal of Differential Equations
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We consider parabolic equations of the form (hence the equation is asymptotically autonomous). ...
We also prove a convergence result for abstract asymptotically autonomous parabolic equations. ...
The decay means that the equation is asymptotically autonomous (both in space and time). ...
doi:10.1016/j.jde.2011.04.002
fatcat:ko3amtd6pnfzvbpw5cli6ihzaa
A constructive converse Lyapunov theorem on asymptotic stability for nonlinear autonomous ordinary differential equations
2005
Dynamical systems
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In this paper we prove a constructive converse theorem on asymptotic stability for nonlinear autonomous ODEs and so improve the 2004 results. ...
An ordinary differential equation's (ODE) equilibrium is asymptotically stable, if and only if the ODE possesses a Lyapunov function, that is, an energy-like function decreasing along any trajectory of ...
Conclusions A constructive converse theorem on asymptotic stability is proved for class C 2 autonomous ODEs. ...
doi:10.1080/14689360500164873
fatcat:t73jrnakxbdnnoss3zper6swc4
Remarks on the Asymptotic Behavior of the Solutions of Certain Non-Autonomous Differential Equations
1972
Proceedings of the Japan Academy
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Remarks on the Asymptotic Behavior o f the Solutions o f Certain Non•Autonomous Differential Equations By Tadayuki HARA Osaka University (Comm. by Kenj iro SHODA, M. J. A., Sept. 12, 1972) 1. ...
In this paper we consider the asymptotic behavior of the solutions of the non-autonomous, nonlinear differential equation ; (1. 1) x=A(t)x+ f (t, x) where x, f are n-dimensional vectors, A(t) is a bounded ...
doi:10.2183/pjab1945.48.549
fatcat:ggtaczxzbffjllxakkx3tf67te
Remarks on the Asymptotic Behavior of the Solutions of Certain Third Order Non-Autonomous Differential Equations
1971
Proceedings of the Japan Academy
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Many results have been obtained on the asymptotic property of autonomous equations of third order and many of these results are summarized in [2] . 2. Assumptions and Theorems. ...
In [4] Swick also considered the asymptotic stability in the large, as t--~ oo, of the zero solution of the differential equations (1.5) x + p(t)x + q(t)g(x) + r(t)h(x) = 0 (1. 6) x + f (x, x, t) ...
doi:10.2183/pjab1945.47.supplementii_915
fatcat:7bz4bamq5jbofl7ubcapgr5j6e
Remarks on the asymptotic behavior of the solutions of certain third order non-autonomous differential equations
1971
Proceedings of the Japan Academy
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Many results have been obtained on the asymptotic property of autonomous equations of third order and many of these results are summarized in [2]. 2. Assumptions and Theorems. ...
In this note we investigate the asymptotic behavior of the solutions of the equation (1.2), and the asymptotic stability in the large of the zero solution of the equation (1.1) under a condition slightly ...
doi:10.3792/pja/1195526295
fatcat:iueyszigbzho3nux3d5ki7qfky
On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations
1973
Publications of the Research Institute for Mathematical Sciences
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On the Asymptotic Behavior of the Solutions of Some Third and Fourth Order Non-Autonomous Differential Equations By Tadayuki HARA*
I. ...
Introduction The purpose of this paper is to investigate the asymptotic behavior of the solutions of non-autonomous differential equations of the form (1.1) x (1.
2) x+a(t)x+b(t)x + c(t)h(x) = p(t, ...
doi:10.2977/prims/1195192447
fatcat:hlbf6blhafaihasarinqha4keu
On the asymptotic behavior of solutions of certain non-autonomous differential equations
1975
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A few authors have studied non-autonomous third order differential equations. K. E. ...
The asymptotic property of solutions of third order differential equations has received a considerable amount of attention during the past two decades, particularly when (1.2) is autonomous. ...
doi:10.18910/12711
fatcat:73jf4obomvhcxg7asi5upnfz5y
Non-autonomous dynamical systems and their applications
2022
Akademos: Revista de Ştiinţă, Inovare, Cultură şi Artă
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This article is devoted to a brief overview of the author's works over the past 10-15 years on non-autonomous dynamic systems and their applications. ...
My results on non-autonomous dynamical systems and their applications are published in three monographs. In this article, we provide an overview of these results. ...
The criterion of asymptotic stability of linear functional-differential equations is proved. ...
doi:10.52673/18570461.21.4-63.02
fatcat:4m45z4tpejearoy2xtc2dbgfgq
Asymptotic Behavior of Perturbed Autonomous Linear Functional Differential Equations
1975
Proceedings of the American Mathematical Society
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Cooke, Linear functional
differential
equations
of asymptotically
autonomous type, J. Differential Equations 7 (1970), 154-174. MR 41 #604.
4. J. ...
Hale, Functional
differential
equations,
Springer-Verlag,
New York, 1971.
5. -,
Linear asymptotically
autonomous
functional
differential
equations,
linear system of differential
equations, ...
doi:10.2307/2040266
fatcat:dnrikf4bmrh3daqzhqeo7itita
Asymptotic behavior of perturbed autonomous linear functional differential equations
1975
Proceedings of the American Mathematical Society
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Cooke, Linear functional
differential
equations
of asymptotically
autonomous type, J. Differential Equations 7 (1970), 154-174. MR 41 #604.
4. J. ...
Hale, Functional
differential
equations,
Springer-Verlag,
New York, 1971.
5. -,
Linear asymptotically
autonomous
functional
differential
equations,
linear system of differential
equations, ...
doi:10.1090/s0002-9939-1975-0369865-1
fatcat:6o73ikhbereqrkatckg2ighdeq
Page 261 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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It can be rec- ommended without reservation to scientists needing information on stability properties of non-autonomous differential equations. ...
It might also be pointed out that the method of limiting sys- tems is only one of the techniques available for studying non- autonomous differential equations. ...
Asymptotically Autonomous Multivalued Differential Equations
1976
Transactions of the American Mathematical Society
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, •) approaches zero as t -*■ °° uniformly on compact subsets of Rd. Other treatments of asymptotically autonomous ordinary differential equations maybe found in [1] - [4] and [6] - [10] . ...
For multivalued functions F and G whose values are nonempty subsets of d-dimensional Euclidean space, Rd, the generalized differential equation 0) x'EF(x) + G(t,x) is said to be asymptotically autonomous ...
Let 0 be a bounded solution of (1) which is defined at least on [0, <*>), and let C denote a compact subset of Rd which contains 0(f) for all t > 0. ...
doi:10.2307/1997410
fatcat:anwkyykf7fbyplxhsfjgp5mgc4
Asymptotically autonomous multivalued differential equations
1976
Transactions of the American Mathematical Society
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The asymptotic behavior of solutions of the perturbed autonomous multivalued differential equation x e F(x) + G(t, x) is examined in relation to the behavior of solutions of the autonomous equation x e ...
, •) approaches zero as t -*■ °° uniformly on compact subsets of Rd. Other treatments of asymptotically autonomous ordinary differential equations maybe found in [1] - [4] and [6] - [10] . ...
For multivalued functions F and G whose values are nonempty subsets of d-dimensional Euclidean space, Rd, the generalized differential equation 0) x'EF(x) + G(t,x) is said to be asymptotically autonomous ...
doi:10.1090/s0002-9947-1976-0435524-5
fatcat:ljjl2nycsnf47mhcrpregxcihm
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