Geodesic
On the Vallée-Poussin problem for singular differential equations with deviating arguments
Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 127-138
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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.
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.
Classification : 34B10
Keywords: singular differential equation with deviating arguments; the Valée-Poussin problem; existence theorem; uniqueness theorem 
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Kiguradze, Ivan; Půža, Bedřich. On the Vallée-Poussin problem for singular differential equations with deviating arguments. Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 127-138. http://geodesic.mathdoc.fr/item/ARM_1997_33_1-2_a13/

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