A Theorem Concerning Uniform Simplification at a Transition Point and the Problem of Resonance.
Abstract
In a certain situation which arises naturally in applications Lim V as epsilon approaches 0 (x, epsilon) = 0 identically for practically all the solutions v of (1), except when F and G are related in a specific way. This exceptional case is called the case of resonance. It is important to find an effectively computable condition for the resonance. B. J. Matkowsky found such a condition. However, so far, it has been mathematically very difficult to prove that the Matkowsky-condition actually guarantees the resonance. The difficulty is due to the fact that a quantity which is decisive in determining the resonance is so small that any existing mathematical tool has failed to dig this quantity out of the differential equation clearly. In this work, we shall provide such a tool.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1980
- Accession Number
- ADA093564
Entities
People
- Yasutaka Sibuya
Organizations
- University of Wisconsin–Madison