Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 201-214
doi:10.1155/BVP.2005.201
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
Abstract
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.