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A note for a second order periodic linear differential equation

✍ Scribed by Dexian Sun

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
244 KB
Volume
15
Category
Article
ISSN
1007-5704

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✦ Synopsis

In this paper, we study the characteristic exponent for a second order linear differential equation x 00 þ qðtÞx ¼ 0 if qðtÞ < 0. As an application, we calculate the characteristic exponents of Eq. x 00 þ qðtÞx ¼ 0 when qðtÞ < 0. The obtained results can be seen as a good generalization of Shi and coworkers [3,4]. We end this paper with some examples which show the simplicity and the high accuracy of our result.

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The equation xЉ t q x t s bx t y 1 , where и designates the greatest integer function, can be described in brief by two amazing properties. First, for certain values of the coefficients, some or all of its solutions are monotone although the corresponding homogeneous equation is clearly oscillatory.