Effects of varying nonlinearity and their singular perturbation flavour

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:248

Article

Elias, U ; Gingold, H

关键词: varying nonlinearity;    convergence of solutions;    delta method;    boundary layer;    interval of existence;    singular perturbations;   

DOI  :  10.1006/jmaa.2000.6912

来源: Elsevier

【 摘 要 】

Autonomous differential equations y + f(y, p) = 0 whose nonlinearity varies with a parameter p are studied. As a prototype, one may think of y + f(0)(y) + \y\(p-1)g(y) = 0. We discuss periodic solutions with initial values taken from Various domains and their different types of convergence as p --> infinity. Equations y - f(y, p) = 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. (C) 2000 Academic Press.

【 授权许可】

Free