**I. Kiguradze and B. Puza**

## On Boundary Value Problems for Functional Differential Equations

**abstract:**

A general theorem (principle of a priori boundedness) on
solvability of the boundary value problem
$$ \frac{dx(t)}{dt}=f(x)(t),\;\;\;h(x)=0 $$
is established, where
$$ f:C([a,b];R^n)\to L([a,b];R^n)\;\;\;\text{and}\;\;\;
h:C([a,b];R^n)\to R^n $$
are continuous operators. As an application,
a two-point boundary value problem for the system of ordinary differential
equations is considered.

**Mathematics Subject Classification:**
34K10.

**Key words and phrases:**
Functional differential equation, boundary value problem,
existence of a solution, principle of a priori boundedness.