On the Vallée-Poussin problem for singular differential equations with deviating arguments

summary: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