Abstract and Applied Analysis
Volume 2004 (2004), Issue 12, Pages 997-1005
An inverse problem for a second-order differential equation in a Banach space
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
Received 29 February 2004
Copyright © 2004 Y. Eidelman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.