Glasnik Matematicki, Vol. 34, No.2 (1999), 223-242.
FUNCTIONAL BOUNDARY VALUE PROBLEMS WITHOUT
Department of Mathematical Analysis, Faculty of Science,
Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic
Abstract. Let J = [0, T] and F :
C0(J) × C0(J)
× R →
L1(J) be an operator.
Existence theorems for the functional differential equation
(F(x, x', x'(t)))(t)
with functional boundary conditions generalizing the
non-homogeneous Dirichlet boundary conditions
and non-homogeneous mixed boundary conditions are given.
Existence results are proved by the Leray-Schauder degree theory
under some sign conditions imposed upon F.
1991 Mathematics Subject Classification.
Key words and phrases. Existence, sign conditions,
Caratheodory conditions, Leray-Schauder degree.
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