Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 201-214

On delay differential equations with nonlinear boundary conditions

Tadeusz Jankowski

Department of Differential Equations, Gdańsk University of Technology, 11/12 Gabriela Narutowicza Street, Gdańsk 80-952, Poland

Received 21 July 2004

Copyright © 2005 Tadeusz Jankowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The monotone iterative method is used to obtain sufficient conditions which guarantee that a delay differential equation with a nonlinear boundary condition has quasisolutions, extremal solutions, or a unique solution. Such results are obtained using techniques of weakly coupled lower and upper solutions or lower and upper solutions. Corresponding results are also obtained for such problems with more delayed arguments. Some new interesting results are also formulated for delay differential inequalities.