For the differential equation \[ u^{(n)}(t)= f(t,u(\tau _{1}(t)),\dots ,u^{(n-1)}(\tau _{n}(t))), \] where the vector function $ f:\ ]a,b[\,\times {R}^{kn} \rightarrow {R}^{k}$ has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established.
@article{107603,
author = {Ivan Kiguradze and Bed\v rich P\r u\v za},
title = {On the Vall\'ee-Poussin problem for singular differential equations with deviating arguments},
journal = {Archivum Mathematicum},
volume = {033},
year = {1997},
pages = {127-138},
zbl = {0914.34064},
mrnumber = {1464307},
language = {en},
url = {http://dml.mathdoc.fr/item/107603}
}
Kiguradze, Ivan; Půža, Bedřich. On the Vallée-Poussin problem for singular differential equations with deviating arguments. Archivum Mathematicum, Tome 033 (1997) pp. 127-138. http://gdmltest.u-ga.fr/item/107603/
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