Boundary Value Problems
Volume 2005 (2005), Issue 3, Pages 263-288
doi:10.1155/BVP.2005.263
On a boundary value problem for nonlinear functional differential equations
Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, Brno 616 62, Czech Republic
Received 21 August 2004; Revised 1 March 2005
Copyright © 2005 Robert Hakl. 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
We consider the problem u′(t)=H(u)(t)+Q(u)(t), u(a)=h(u), where H,Q:C([a,b];R)→L([a,b];R) are, in general, nonlinear
continuous operators, H∈ℋabαβ(g0,g1,p0,p1), and h:C([a,b];R)→R is a continuous functional. Efficient conditions sufficient for the
solvability and unique solvability of the problem considered are established.