On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations

A. Lomtatidze, Masaryk University, Brno, Czech Republic
Z. Oplustil, Masaryk University, Brno, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ., No. 16. (2004), pp. 1-21.

Abstract: Unimprovable efficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem
$$
u^{\prime}(t)=\ell(u)(t)+q(t), \ \ \ \ u(a)=h(u)+c,
$$
where $\ell:C([a,b];\mathbb{R})\rightarrow L([a,b];\mathbb{R})$ is a linear bounded operator, $h:C([a,b];\mathbb{R})\rightarrow \mathbb{R}$ is a linear bounded functional, $q\in L([a,b];\mathbb{R})$ and $c>0$.

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