Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 201-214
On delay differential equations with nonlinear boundary conditions
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.