International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 509-516
doi:10.1155/S0161171291000698
Existence of solutions of boundary value problems for functional differential equations
University of Ioannina, Department of Mathematics, Ioannina, Greece
Received 27 September 1989; Revised 10 October 1990
Copyright © 1991 S. K. Ntouyas and P. Ch. Tsamatos. 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.
Abstract
In this paper, using a simple and classical application of the Leray-Schauder
degree theory, we study the existence of solutions of the following boundary value
problem for functional differential equations
x″(t)+f(t,xt,x′(t))=0, t∈[0,T]x0+αx′(0)=hx(T)+βx′(T)=η
where f∈C([0,T]×Cr×ℝn,ℝn), h∈Cr, η∈ℝn and α, β, are real constants.