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

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.