BOUNDS FOR SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
Abstract
Most of the known explicit bounds, as well as criteria for global existence and boundedness, can be obtained from comparison theorems, together with a detailed analysis of the resulting first order differential equations. The same approach also yields information on the approach of a solution to a limit. The bounds given are sometimes difficult or impossible to calculate explicitly, but it is possible to give slightly weaker bounds, which are more easily calculated. The main conclusion to be drawn is that the comparison method provides not only a powerful tool for obtaining bounds for solutions, but also a unified approach to many such problems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1961
- Accession Number
- AD0269323
Entities
People
- Fred Brauer
Organizations
- University of Wisconsin–Madison