I. Kiguradze and B. Puza

On Boundary Value Problems for Functional Differential Equations

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.