International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 625-644
Boundary value problems in time for wave equations on
Department of Mathematics, Iowa State University, Ames 50011, Iowa, USA
Received 5 December 1989
Copyright © 1990 M. W. Smiley and A. M. Fink. 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.
Let denote the linear operator associated with the radially symmetric form of the wave operator together with the side conditions of decay to zero as and -periodicity in time. Thus , when there are space variables. For let and denote the weighted space with weight function . It is shown that is a Fredholm operator from onto with non-negative index depending on . If then the index is . In addition it is shown that has a bounded partial inverse , with all spaces weighted by the function . This provides a key ingredient for the analysis of nonlinear problems via the method of alternative problems.