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Keywords:
singular differential equation with deviating arguments; the Valée-Poussin problem; existence theorem; uniqueness theorem
singular differential equation with deviating arguments; the Valée-Poussin problem; existence theorem; uniqueness theorem
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.
References:
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