Abstract. The functional differential equation
(x'(t) + L(x')(t))' = F(x)(t)together with functional boundary conditions is considered. Existence results are proved by the Leray-Schauder degree and the Borsuk theorem for α-condensing operators. We demonstrate on examples that our existence assumptions are optimal.
1991 Mathematics Subject Classification. 34K15, 34B15.
Key words and phrases. Functional boundary value problem, neutral equation, existence, α-condensing operator, Leray-Schauder degree, Borsuk theorem.