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Keywords:
linear functional differential equations; differential equations with deviating arguments; initial value problems
Summary:
The nonimprovable sufficient conditions for the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)=c, \] where $\ell \: C(I;\mathbb{R})\rightarrow L(I;\mathbb{R})$ is a linear bounded operator, $q\in L(I;\mathbb{R})$, $c\in \mathbb{R}$, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator $\ell $ is not of Volterra’s type with respect to the point $a$.
References:
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