Functional boundary value problems without growth restrictions

Glasnik Matematicki, Vol. 34, No.2 (1999), 223-242.

FUNCTIONAL BOUNDARY VALUE PROBLEMS WITHOUT GROWTH RESTRICTIONS

Svatoslav Stanek

Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic
e-mail: stanek@risc.upol.cz

Abstract. Let J = [0, T] and F : C⁰(J) × C⁰(J) × R → L₁(J) be an operator. Existence theorems for the functional differential equation

(g(x'(t)))' = (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. 34K10.

Key words and phrases. Existence, sign conditions, Caratheodory conditions, Leray-Schauder degree.

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