A. Lomtatidze and P. Vodstrčil

On Nonnegative Solutions of Second Order Linear Functional Differential Equations

abstract:
On the interval $[a,b]$, we consider the boundary value problems
$$ u^{\prime\prime}(t) = \ell (u)(t) + q(t); \qquad u(a)=0, \quad u(b)=0 $$ and
$$ u^{\prime\prime}(t) = \ell (u)(t) + q(t); \qquad u(a)=0, \quad u^{\prime}(b)=0, $$
where $\ell : C([a,b];\R) \rightarrow L([a,b];\R)$ and $q \in L([a,b];\R)$.
The existence and uniqueness of nonnegative solutions of these problems are
studied. 

Mathematics Subject Classification: 34K06, 34K10

Key words and phrases: Second order linear functional differential equation, two--point BVP, nonnegative solution