Vol. 54, No. 1, 1974

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Singular perturbation of a time-dependent Cauchy problem in a Hilbert space

Larry Eugene Bobisud and James Calvert

Vol. 54 (1974), No. 1, 45–53
Abstract

Let A be a self-adjoint operator, not necessarily bounded, in the Hilbert space H, with resolution of the identity Eλ. Define h(t,A) = −∞h(t,λ)dEλ. It is shown that as 𝜖 0+ the solution of the abstract problem 𝜖U𝜖′′ + bU𝜖+ h(t,A)U𝜖 = 0,U𝜖(0) = x0,U𝜖(0) = x1 tends in the norm of H to the solution of bU0+ h(t,A)U0 = 0,U0(0) = x0 for data x0,x1 in a dense subset of H.

Mathematical Subject Classification
Primary: 34G05
Milestones
Received: 2 April 1973
Published: 1 September 1974
Authors
Larry Eugene Bobisud
James Calvert