Vol. 36, No. 3, 1971

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Singular perturbations of differential equations in abstract spaces

Hussain Sayid Nur

Vol. 36 (1971), No. 3, 775–780
Abstract

In a recent paper, Kisynski studied the solutions of the abstract Cauchy problem 𝜖x⋅⋅(t) + x(t) + Ax(t) = 0, x(0) = x0 and x(0) = x1 where 0 t T,𝜖 > 0 is small parameter and A is a nonnegative self-adjoint operator in a Hilbert space H. With the aid of the functional calculus of the operator A, he has showed that as 𝜖 0 the solution of this problem converges to the solution of the unperturbed Cauchy problem x(t) + Ax(t) = 0, x(0) = x0. Smoller has proved the same result for equation of higher order.

The purpose of this paper is to study the solution of a similar problem and allowing the operator A to depend on t.

Mathematical Subject Classification
Primary: 34.95
Milestones
Received: 2 December 1969
Published: 1 March 1971
Authors
Hussain Sayid Nur