The Connection between the Characteristic Roots and the Corresponding Solutions of a Single Linear Differential Equation with Comparable Coefficients

✍ Scribed by M. H. Lantsman

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 987 KB
• Volume: 204
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19992040109

✦ Synopsis

Given 8 linear differentid equation of the form dn) + 131 (t)z("'l) + . -+ a,,(t)z = 0 with variable coefficients defined on the poaitive aemi-sxis for t > 1. We denote its fundamental aet of solutions (FSS) by {exp [Jri(t) dt] } (i = 1,2,. . . ,n). In this paper we look for the asymptotic connection (aa t + 00) between the logarithmic derivatives ri(t) of an FSS and of the roots of the characterintic equation y" + al(t)yn'' + ... + an(t) = 0. We mainly consider the case when the coefficients of the equation and the characteristic roots are comparable and have the power order of gruwth for t + 00. We diacuse the conditions when the functions ri(t) are equivalent to the corresponding roots &(t) of the chsracteristic equation as t -3 00.