A note on non-autonomous scalar functional differential equations with small delay

被引：2
|
作者：
Alonso, AI
Obaya, R
Sanz, AM
机构：
[1] ETS Ingn Ind, Dept Matemat Aplicada, E-47011 Valladolid, Spain
[2] Univ Valladolid, Fac Ciencias, Dept Anal Matemat & Didoct Matemat, E-47005 Valladolid, Spain
来源：
COMPTES RENDUS MATHEMATIQUE | 2005年 / 340卷 / 02期
关键词：
D O I：
10.1016/j.crma.2004.11.027
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the minimal sets in the skew-product semiflows generated from a non-autonomous scalar functional differential equation with a small delay are all almost automorphic extensions of the base. This result is not true for arbitrary delay equations. The point is that, for a small delay, so-called special solutions exist and permit us to tackle the problem by means of some related scalar ODE's for which the study is much simpler. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
引用
收藏
页码：155 / 160
页数：6
相关论文
共 50 条
  • [1] Non-autonomous Functional Differential Equations and Applications
    Novo, Sylvia
    Obaya, Rafael
    [J]. STABILITY AND BIFURCATION THEORY FOR NON-AUTONOMOUS DIFFERENTIAL EQUATIONS, CETRARO, ITALY 2011, 2013, 2065 : 185 - 263
  • [2] Periodic Solutions for Non-Autonomous Neutral Functional Differential Equations with Finite Delay
    Zitane M.
    [J]. Acta Mathematica Vietnamica, 2017, 42 (3) : 533 - 550
  • [3] PERSISTENCE IN NON-AUTONOMOUS QUASIMONOTONE PARABOLIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DELAY
    Obaya, Rafael
    Sanz, Ana M.
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3947 - 3970
  • [4] A non-autonomous bifurcation theory for deterministic scalar differential equations
    Nunez, Carmen
    Obaya, Rafael
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2008, 9 (3-4): : 701 - 730
  • [5] Bifurcations in non-autonomous scalar equations
    Langa, JA
    Robinson, JC
    Suárez, A
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (01) : 1 - 35
  • [6] Existence of solutions of non-autonomous second order functional differential equations with infinite delay
    Henriquez, Hernan R.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (10) : 3333 - 3352
  • [7] SKEW-PRODUCT SEMIFLOWS FOR NON-AUTONOMOUS PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DELAY
    Novo, Sylvia
    Nunez, Carmen
    Obaya, Rafael
    Sanz, Ana M.
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (10) : 4291 - 4321
  • [8] Non-autonomous nonlocal partial differential equations with delay and memory
    Xu, Jiaohui
    Zhang, Zhengce
    Caraballo, Tomas
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 270 : 505 - 546
  • [9] Periodic solutions for a class of non-autonomous differential delay equations
    Cheng, Rong
    Xu, Junxiang
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (06): : 793 - 809
  • [10] Periodic solutions for a class of non-autonomous differential delay equations
    Rong Cheng
    Junxiang Xu
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2009, 16
12345