Retract principle for neutral functional differential equations Original Research Article

The investigation of asymptotic behaviour of solutions of ordinary differential equations is often based on the application of the retract principle. Initially developed for ordinary differential equations, this technique was extended to other classes of equations. Not answered remains a problem concerning the possibility of extending this principle to neutral differential equations. The goal of the present paper is to partially fill this gap and develop a corresponding technique for the application of this principle. The applicability of the main result is illustrated on a nonlinear equation and sufficient conditions for existence of a positive solution are derived.