Representation of the general solution of the degenerate initial value problem for quasilinear functional-differential equations with several deviations of the argument. (Russian) Zbl 0625.34075
Functional-differential equations and their applications, Collect. sci. Works, Kiev 1985, 87-108 (1985).
[For the entire collection see Zbl 0586.00013.]
The author discusses the asymptotic behavior near zero of \(C^ 1\)-smooth solutions to the Cauchy problem \[ \sum^{m}_{j=0}t^{\mu_ j}B_ j(t,y(\alpha_ 0t),...,y(\alpha_ mt))y'(\alpha_ jt)=F(t,y(\alpha_ 0t),...,y(\alpha_ mt)),\quad y(0)=0, \] where \(\alpha_ j>0\); \(0<\mu_ 0<\mu_ 1\leq \mu_ 2...\leq \mu_ m\) and \(\mu_ 0<1\).
The author discusses the asymptotic behavior near zero of \(C^ 1\)-smooth solutions to the Cauchy problem \[ \sum^{m}_{j=0}t^{\mu_ j}B_ j(t,y(\alpha_ 0t),...,y(\alpha_ mt))y'(\alpha_ jt)=F(t,y(\alpha_ 0t),...,y(\alpha_ mt)),\quad y(0)=0, \] where \(\alpha_ j>0\); \(0<\mu_ 0<\mu_ 1\leq \mu_ 2...\leq \mu_ m\) and \(\mu_ 0<1\).
Reviewer: R.R.Akhmerov
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
