CRITICAL LINEAR DIFFERENCE EQUATIONS: A STUDY IN PATHOLOGY,
Abstract
The paper discusses the structure of solutions of the linear scaler difference equation x(t + h) = x(t) + f(t), and in part its relationship to the differential equation x dot (t) = f(t). It is shown that the structure of solutions of the difference equation is critically dependent on h. For example, given f periodic, there is a dense set of h's for which there is not even a generalized periodic solution, no matter how smooth f is. Conditions on f for boundedness and uniform continuity of solutions are obtained and an example is presented to show that if f is almost periodic and the solution is bounded, the solution need not be almost periodic. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0697644
Entities
People
- Anthony J. Schaeffer
- James J. Hurt
Organizations
- University of Iowa