2003, 2003(Special): 100-107. doi: 10.3934/proc.2003.2003.100

Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays

1. 

Department of Mathematics, Faculty of Sciences, Ankara University, 06100 Tandoğan-Ankara, Turkey

2. 

Department of Mathematics and Computing, University of Veszprém, P.O. Box 158, 8201 Veszprém, Hungary

Received  August 2002 Revised  March 2003 Published  April 2003

Sufficient conditions are given for the asymptotic constancy of the solutions of a nonhomogeneous linear delay differential equation with unbounded delays. Moreover, it is shown that the limits of the solutions, as $t \to \infty$, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.
Citation: Hüseyin Bereketoğlu, Mihály Pituk. Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays. Conference Publications, 2003, 2003 (Special) : 100-107. doi: 10.3934/proc.2003.2003.100
[1]

Loïs Boullu, Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. Oscillations and asymptotic convergence for a delay differential equation modeling platelet production. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2417-2442. doi: 10.3934/dcdsb.2018259

[2]

Ábel Garab. Unique periodic orbits of a delay differential equation with piecewise linear feedback function. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2369-2387. doi: 10.3934/dcds.2013.33.2369

[3]

Michael Scheutzow. Exponential growth rate for a singular linear stochastic delay differential equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1683-1696. doi: 10.3934/dcdsb.2013.18.1683

[4]

Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017

[5]

Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159

[6]

Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73

[7]

Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013

[8]

Kazuki Himoto, Hideaki Matsunaga. The limits of solutions of a linear delay integral equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3033-3048. doi: 10.3934/dcdsb.2020050

[9]

Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1103-1110. doi: 10.3934/dcdss.2020392

[10]

P. Dormayer, A. F. Ivanov. Symmetric periodic solutions of a delay differential equation. Conference Publications, 1998, 1998 (Special) : 220-230. doi: 10.3934/proc.1998.1998.220

[11]

Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variable. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 495-512. doi: 10.3934/naco.2020040

[12]

Arturo de Pablo, Guillermo Reyes, Ariel Sánchez. The Cauchy problem for a nonhomogeneous heat equation with reaction. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 643-662. doi: 10.3934/dcds.2013.33.643

[13]

Victor Ginting. An adjoint-based a posteriori analysis of numerical approximation of Richards equation. Electronic Research Archive, 2021, 29 (5) : 3405-3427. doi: 10.3934/era.2021045

[14]

Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1663-1681. doi: 10.3934/dcdsb.2013.18.1663

[15]

Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689

[16]

A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple state-dependent delays. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2701-2727. doi: 10.3934/dcds.2012.32.2701

[17]

Tomás Caraballo, Renato Colucci, Luca Guerrini. Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2639-2655. doi: 10.3934/dcdsb.2018268

[18]

Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223

[19]

Chunqing Lu. Asymptotic solutions of a nonlinear equation. Conference Publications, 2003, 2003 (Special) : 590-595. doi: 10.3934/proc.2003.2003.590

[20]

Tuhin Ghosh, Karthik Iyer. Cloaking for a quasi-linear elliptic partial differential equation. Inverse Problems and Imaging, 2018, 12 (2) : 461-491. doi: 10.3934/ipi.2018020

 Impact Factor: 

Metrics

  • PDF downloads (121)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]