✦ LIBER ✦

Effects of Varying Nonlinearity and Their Singular Perturbation Flavour

✍ Scribed by U. Elias; H. Gingold

Book ID: 102590089
Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 138 KB
Volume: 248
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6912

No coin nor oath required. For personal study only.

✦ Synopsis

Autonomous differential equations y q f y, p s 0 whose nonlinearity varies Y Ž . with a parameter p are studied. As a prototype, one may think of y q f y q 0 < < py 1 Ž . y g y s 0. We discuss periodic solutions with initial values taken from various domains and their different types of convergence as p ª ϱ. Equations y Y y Ž . Ž . f y, p s 0, yf y, p ) 0 are similarly discussed, with the ''period'' of a solution replaced by its ''maximal interval of existence.'' The study shows a natural link to singularly perturbed problems. It turns out that the family of ODEs under consideration are essentially a family of singularly perturbed problems. Solutions may develop ''kinks'' and higher order derivatives of solutions possess ''boundary layers,'' namely sets of non-uniform convergence. Similarities and differences between this family and the more common singularly perturbed problems which abound in the literature emerge.

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