**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.

Communicated by L. Hatvani.
| Received on 2003-09-30 Appeared on 2004-08-31 |

**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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