**Hana Štěpánková**

## On Nonnegative Solutions of Initial Value Problems for Second

Order Linear Functional Differential Equations

**Abstract:**

Optimal sufficient conditions are established for the existence and uniqueness
of a nonnegative solution of the initial value problem

$$u''(t)=\ell(u)(t)+q(t),\quad u(a)=c_1,\quad u'(a)=c_2,$$

where $\ell$ is nonpositive $a$-Volterra operator.

**Keywords:**

Second order linear functional differential equation, initial value problem,
nonnegative solution.

**MSC 2000:** 34K06, 34K05