A. Lomtatidze, Z. Opluštil, and J. Šremr

On a Nonlocal Boundary Value Problem for First Order Linear Functional Differential Equations

abstract:
Efficient sufficient conditions are established for the unique solvability of the problem $$ u\de(t)=\ell(u)(t)+q(t), \;\;\; u(a)= h(u)+c, $$ where $\ell:C([a,b];\m{R})\to L([a,b];\m{R})$ and
$h:C([a,b];\m{R})\to\m{R}$ are linear bounded operatos, $q\in L([a,b];\m{R})$, and $c\in\m{R}$.

Mathematics Subject Classification: 34K06, 34K10

Key words and phrases: Linear functional differential equation, nonlocal boundary value problem, existence, uniqueness