Vol. 53, No. 2, 1974

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ISSN: 0030-8730
Existence, uniqueness and limiting behavior of solutions of a class of differential equations in Banach space

John Lagnese

Vol. 53 (1974), No. 2, 473–485
Abstract

Let X be a Banach space (real or complex) and An and B be linear operators in X with D(B) D(An),n = 1,2, . The following note is concerned with existence and uniqueness of solutions of the problem

d-[(I − A )u(t)]− Bu(t) = 0, (t > 0),  u(0) = u ,
dt      n                                 0
(1.1)

and the limiting behavior of these solutions as the operators An tend to zero in a sense to be specified. We will show that for a large class of operators the problem (1.1) is well posed and that its solutions tend to the solution of the problem

du(t)− Bu (t) = 0, (t > 0), u(0) = u .
dt                              0
(1.2)

Mathematical Subject Classification 2000
Primary: 34G05
Secondary: 35L99
Milestones
Received: 30 May 1972
Revised: 20 February 1973
Published: 1 August 1974
Authors
John Lagnese