Filters








34,688 Hits in 3.7 sec

On Asymptotically Autonomous Retarded Functional Differential Equations

Gyula Farkas
2001 Journal of Mathematical Analysis and Applications  
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

Boris S. Klebanov
1997 Topological Methods in Nonlinear Analysis  
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

Juraj Földes, P. Poláčik
2011 Journal of Differential Equations  
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

S. F. Hafstein *
2005 Dynamical systems  
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

Tadayuki HARA
1972 Proceedings of the Japan Academy  
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

Minoru YAMAMOTO
1971 Proceedings of the Japan Academy  
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

Minoru Yamamoto
1971 Proceedings of the Japan Academy  
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

Tadayuki Hara
1973 Publications of the Research Institute for Mathematical Sciences  
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

Tadayuki Hara
1975
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

David Cheban, Moldova State University
2022 Akademos: Revista de Ştiinţă, Inovare, Cultură şi Artă  
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

Richard B. Evans
1975 Proceedings of the American Mathematical Society  
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

Richard B. Evans
1975 Proceedings of the American Mathematical Society  
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  
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

James P. Foti
1976 Transactions of the American Mathematical Society  
, •) 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

James P. Foti
1976 Transactions of the American Mathematical Society  
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
« Previous Showing results 1 — 15 out of 34,688 results