Vol. 90, No. 2, 1980

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ISSN: 0030-8730
Boundary value problems for partial functional differential equations

Samuel Murray Rankin, III

Vol. 90 (1980), No. 2, 459–468
Abstract

Sufficient conditions are given to ensure the existence of solutions for the boundary value problem

               ∫
t
y(t) = T(t)ϕ (0)+ 0 T(t− s)F(ys)ds  0 ≦ t ≦ b
(1)

M y0 + Nyb = ψ, ψ ∈ C (= C([− r,0];B) by def.).       (*)

It is assumed that T(t), t 0, is a strongly continuous semigroup of bounded linear operators on the Banach space B and T(t), t 0, has infinitesimal generator A. The function F is continuous from C to B and M and N are bounded linear operators defined on C.

Mathematical Subject Classification 2000
Primary: 34K10
Secondary: 45K05
Milestones
Received: 8 June 1977
Revised: 18 October 1978
Published: 1 October 1980
Authors
Samuel Murray Rankin, III