ON A SINGULAR POINT OF BRIOT-BOUQUET TYPE OF A SYSTEM OF TWO ORDINARY NONLINEAR DIFFERENTIAL EQUATIONS.
Abstract
The singular points of Briot-Bouquet type of a system of ordinary nonlinear differential equations written in the form x dw/dx = h(x, w), h(0, 0) = 0, have been studied by diverse authors since C. H. Briot and J. C. Bouquet. Here, w is an n-dimensional column vector and h(x, w) is an n-dimensional column vector function holomorphic and bounded in (x, w) in a neighborhood of (0, 0). However, as far as I know, it has not yet been studied, except for n = 1, when the eigenvalues of the matrix h sub w (0, 0) are all zero. In this note the author studies the case for n = 2 under certain hypotheses. For convenience, the paper is divided into three parts. Part I is concerned with the construction of a formal transformation. In Part II formal solutions are constructed of diverse types depending on two arbitrary constants. Part III considers the analytical meaning of each of those formal solutions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1966
- Accession Number
- AD0648173
Entities
People
- Masahiro Iwano
Organizations
- University of Wisconsin–Madison