Abstract and Applied Analysis
Volume 2004 (2004), Issue 12, Pages 997-1005
doi:10.1155/S108533750440308X

An inverse problem for a second-order differential equation in a Banach space

Abstract

We consider the problem of determining the unknown term in the right-hand side of a second-order differential equation with unbounded operator generating a cosine operator function from the overspecified boundary data. We obtain necessary and sufficient conditions of the unique solvability of this problem in terms of location of the spectrum of the unbounded operator and properties of its resolvent.