
Previous Article
Stabilization of a hyperbolic/elliptic system modelling the viscoelasticgravitational deformation in a multilayered Earth
 PROC Home
 This Issue

Next Article
Hartmantype conditions for multivalued Dirichlet problem in abstract spaces
Subexponential growth rates in functional differential equations
1.  Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland 
2.  School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9,, Ireland 
References:
[1] 
J. A. D. Appleby, M. J. McCarthy and A. Rodkina, Growth rates of delaydifferential equations and uniform Euler schemes, Difference equations and applications, (eds. M. Bohner et al.), UǧurBahçeşehir Univ. Publ. Co., Istanbul, (2009), 117124. Google Scholar 
[2] 
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge University Press, Cambridge, 1987. Google Scholar 
[3] 
J. R. Graef, Oscillation, nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order, J. Math. Anal. Appl., 60 (1977), 398409. Google Scholar 
[4] 
G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics, 34, Cambridge University Press, Cambridge, 1990. Google Scholar 
[5] 
P. Hartman and A. Wintner, Asymptotic integration of ordinary nonlinear differential equations, Amer. J. Math., 77 (1955), 692724. Google Scholar 
[6] 
P. Hartman, Ordinary differential equations, $2^{nd}$ edition, SIAM, Philadelphia, 2002. Google Scholar 
[7] 
T. Kusano and H. Onose, Oscillatory and asymptotic behavior of sublinear retarded differential equations Hiroshima Math. J., 4 (1974), 343355. Google Scholar 
[8] 
M. Pituk, The HartmanWintner Theorem for Functional Differential Equations, J. Differential Equations, 155 (1), (1999), 116. Google Scholar 
show all references
References:
[1] 
J. A. D. Appleby, M. J. McCarthy and A. Rodkina, Growth rates of delaydifferential equations and uniform Euler schemes, Difference equations and applications, (eds. M. Bohner et al.), UǧurBahçeşehir Univ. Publ. Co., Istanbul, (2009), 117124. Google Scholar 
[2] 
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge University Press, Cambridge, 1987. Google Scholar 
[3] 
J. R. Graef, Oscillation, nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order, J. Math. Anal. Appl., 60 (1977), 398409. Google Scholar 
[4] 
G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics, 34, Cambridge University Press, Cambridge, 1990. Google Scholar 
[5] 
P. Hartman and A. Wintner, Asymptotic integration of ordinary nonlinear differential equations, Amer. J. Math., 77 (1955), 692724. Google Scholar 
[6] 
P. Hartman, Ordinary differential equations, $2^{nd}$ edition, SIAM, Philadelphia, 2002. Google Scholar 
[7] 
T. Kusano and H. Onose, Oscillatory and asymptotic behavior of sublinear retarded differential equations Hiroshima Math. J., 4 (1974), 343355. Google Scholar 
[8] 
M. Pituk, The HartmanWintner Theorem for Functional Differential Equations, J. Differential Equations, 155 (1), (1999), 116. Google Scholar 
[1] 
Frank Blume. Realizing subexponential entropy growth rates by cutting and stacking. Discrete & Continuous Dynamical Systems  B, 2015, 20 (10) : 34353459. doi: 10.3934/dcdsb.2015.20.3435 
[2] 
Tomás Caraballo, Gábor Kiss. Attractivity for neutral functional differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 17931804. doi: 10.3934/dcdsb.2013.18.1793 
[3] 
Marie Doumic, Miguel Escobedo. Time asymptotics for a critical case in fragmentation and growthfragmentation equations. Kinetic & Related Models, 2016, 9 (2) : 251297. doi: 10.3934/krm.2016.9.251 
[4] 
Vitalii G. Kurbatov, Valentina I. Kuznetsova. On stability of functional differential equations with rapidly oscillating coefficients. Communications on Pure & Applied Analysis, 2018, 17 (1) : 267283. doi: 10.3934/cpaa.2018016 
[5] 
Yongqiang Suo, Chenggui Yuan. Large deviations for neutral stochastic functional differential equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 23692384. doi: 10.3934/cpaa.2020103 
[6] 
Olesya V. Solonukha. On nonlinear and quasiliniear elliptic functional differential equations. Discrete & Continuous Dynamical Systems  S, 2016, 9 (3) : 869893. doi: 10.3934/dcdss.2016033 
[7] 
Pierluigi Benevieri, Alessandro Calamai, Massimo Furi, Maria Patrizia Pera. On general properties of retarded functional differential equations on manifolds. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 2746. doi: 10.3934/dcds.2013.33.27 
[8] 
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31273144. doi: 10.3934/dcdsb.2017167 
[9] 
David Lipshutz. Exit time asymptotics for small noise stochastic delay differential equations. Discrete & Continuous Dynamical Systems, 2018, 38 (6) : 30993138. doi: 10.3934/dcds.2018135 
[10] 
Qingwu Gao, Zhongquan Huang, Houcai Shen, Juan Zheng. Asymptotics for randomtime ruin probability in a timedependent renewal risk model with subexponential claims. Journal of Industrial & Management Optimization, 2016, 12 (1) : 3143. doi: 10.3934/jimo.2016.12.31 
[11] 
John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91101. doi: 10.3934/proc.2011.2011.91 
[12] 
Daniel Balagué, José A. Cañizo, Pierre Gabriel. Fine asymptotics of profiles and relaxation to equilibrium for growthfragmentation equations with variable drift rates. Kinetic & Related Models, 2013, 6 (2) : 219243. doi: 10.3934/krm.2013.6.219 
[13] 
Burcu Gürbüz. A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021069 
[14] 
PietroLuciano Buono, V.G. LeBlanc. Equivariant versal unfoldings for linear retarded functional differential equations. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 283302. doi: 10.3934/dcds.2005.12.283 
[15] 
Ovide Arino, Eva Sánchez. A saddle point theorem for functional statedependent delay differential equations. Discrete & Continuous Dynamical Systems, 2005, 12 (4) : 687722. doi: 10.3934/dcds.2005.12.687 
[16] 
Kai Liu. On regularity of stochastic convolutions of functional linear differential equations with memory. Discrete & Continuous Dynamical Systems  B, 2020, 25 (4) : 12791298. doi: 10.3934/dcdsb.2019220 
[17] 
Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 10051023. doi: 10.3934/dcds.2009.24.1005 
[18] 
Nguyen Minh Man, Nguyen Van Minh. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Communications on Pure & Applied Analysis, 2004, 3 (2) : 291300. doi: 10.3934/cpaa.2004.3.291 
[19] 
R.S. Dahiya, A. Zafer. Oscillatory theorems of nth order functional differential equations. Conference Publications, 2001, 2001 (Special) : 435443. doi: 10.3934/proc.2001.2001.435 
[20] 
Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with statedependent delay. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 39393961. doi: 10.3934/dcds.2017167 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]