scholarly journals Advanced-Retarded Differential Equations in Quantum Photonic Systems

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Unai Alvarez-Rodriguez ◽  
Armando Perez-Leija ◽  
Iñigo L. Egusquiza ◽  
Markus Gräfe ◽  
Mikel Sanz ◽  
...  
Keyword(s):  
Differential Equations ◽  
Retarded Differential Equations

scholarly journals Retarded differential equations with piecewise constant delays

1984 ◽  
Vol 99 (1) ◽  
pp. 265-297 ◽  
Author(s):  
Kenneth L Cooke ◽  
Joseph Wiener
Keyword(s):  
Differential Equations ◽  
Piecewise Constant ◽  
Retarded Differential Equations

scholarly journals Retarded differential equations

2000 ◽  
Vol 125 (1-2) ◽  
pp. 309-335 ◽  
Author(s):  
Christopher T.H. Baker
Keyword(s):  
Differential Equations ◽  
Retarded Differential Equations

scholarly journals Asymptotic behavior of solutions of retarded differential equations

1983 ◽  
Vol 88 (2) ◽  
pp. 247-247 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas ◽  
I. P. Stavroulakis
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Retarded Differential Equations

Asymptotic stability of the zero solution for degenerate retarded differential equations

2009 ◽  
Vol 70 (3) ◽  
pp. 1415-1421 ◽  
Author(s):  
Xian-Feng Zhou ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Zero Solution ◽  
Retarded Differential Equations

scholarly journals Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations

1999 ◽  
Vol 4 (3) ◽  
pp. 169-194 ◽  
Author(s):  
Gabriele Gühring ◽  
Frank Räbiger
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Evolution Equation ◽  
Unique Solution ◽  
Evolution Equations ◽  
Bounded Solution ◽  
Mild Solutions ◽  
Asymptotic Properties ◽  
Yosida Operator ◽  
Retarded Differential Equations

We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation(d/dt)u(t)=Au(t)+B(t)u(t)+f(t),t∈ℝ, where(A,D(A))is a Hille-Yosida operator on a Banach spaceX,B(t),t∈ℝ, is a family of operators inℒ(D(A)¯,X)satisfying certain boundedness and measurability conditions andf∈L loc 1(ℝ,X). The solutions of the corresponding homogeneous equations are represented by an evolution family(UB(t,s))t≥s. For various function spacesℱwe show conditions on(UB(t,s))t≥sandfwhich ensure the existence of a unique solution contained inℱ. In particular, if(UB(t,s))t≥sisp-periodic there exists a unique bounded solutionusubject to certain spectral assumptions onUB(p,0),fandu. We apply the results to nonautonomous semilinear retarded differential equations. For certainp-periodic retarded differential equations we derive a characteristic equation which is used to determine the spectrum of(UB(t,s))t≥s.

scholarly journals Attractiveness and Hopf bifurcation for retarded differential equations

2003 ◽  
Vol 2 (2) ◽  
pp. 147-158 ◽  
Author(s):  
R. Ouifki ◽  
◽  
M. L. Hbid ◽  
O. Arino ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Differential Equations ◽  
Retarded Differential Equations
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