Bifurcation properties for a sequence of approximation of delay equations. Arino, O. & Benkhalti, R. J. Math. Anal. Appl., 171(2):377–388, 1992. abstract bibtex The purpose of the paper is to investigate properties of the differential equations $\dot x=λf(x(t),$ $x(t-1))$ and its approximation by difference equations. In section II the authors show that in any segment $[ǎrphi,\psi]$ of initial values (where $ǎrphi<0<\psi)$ there is at least one initial value of an oscillating solution which is the limit of a sequence of initial values for the approximating equations. The results in section III contain information about bifurcation of Rabinowitz type.
@Article{ArinoBenkhalti1992,
author = {Arino, Ovide and Benkhalti, Rachid},
title = {Bifurcation properties for a sequence of approximation of delay equations},
journal = {J. Math. Anal. Appl.},
year = {1992},
volume = {171},
number = {2},
pages = {377--388},
issn = {0022-247X},
abstract = {The purpose of the paper is to investigate
properties of the differential equations $\dot
x=\lambda f(x(t),$ $x(t-1))$ and its approximation
by difference equations. In section II the authors
show that in any segment $[\varphi,\psi]$ of initial
values (where $\varphi<0<\psi)$ there is at least
one initial value of an oscillating solution which
is the limit of a sequence of initial values for the
approximating equations. The results in section III
contain information about bifurcation of Rabinowitz
type.},
classmath = {*34K15 Qualitative theory of solutions of functional-differential equations 34C23 Bifurcation (periodic solutions) 34A45 Theoretical approximation of solutions of ODE 34A47 Bifurcation 39A10 Difference equations },
coden = {JMANAK},
fjournal = {Journal of Mathematical Analysis and Applications},
keywords = {delay differential equations; approximation by difference equations; oscillating solution; bifurcation of Rabinowitz type},
mrclass = {34K15},
mrnumber = {93j:34098},
mrreviewer = {Xiao Biao Lin},
reviewer = {G.Karakostas (Ioannina)},
}
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