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Global Behavior of Solutions of a Certain Nth Order Differential Equation in the Vicinity of an Irregular Singular Point

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Differential Equations and Nonlinear Mechanics

Part of the book series: Mathematics and Its Applications ((MAIA,volume 528))

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Abstract

This paper is devoted to the global behavior of solutions of the nth order differential equation

$${z^n}\left( {{a_n} + {b_n}{z^m}} \right)\frac{{{d^n}y}}{{d{z^n}}} + {z^{n - 1}}\left( {{a_{n - 1}} + {b_{n - 1}}{z^m}} \right)\frac{{{d^{n - 1}}y}}{{d{z^{n - 1}}}} + \sum\limits_{k = 0}^{n = 2} {{z_k}} \left( {{a_k} + {b_k}{z^m} + {c_k}{z^{2m}}} \right)\frac{{{d^k}y}}{{d{z^k}}} = 0$$

Here, m is an arbitrary positive integer. The variable z and the constants a n , b n a n-1 ,b n-1 and a k ,b k ,c k (k = 0,1,2,…,n – 2) are complex with a n ≠ 0, b n ≠ 0, c n–2 ≠ 0. We shall also assume that the difference of no two roots of the indicial equation about the regular singular part z = 0 is congruent to zero module m.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Ball State University, Muncie, Indiana, 47306, USA

    T. K. Puttaswamy

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  1. T. K. Puttaswamy
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Editor information

Editors and Affiliations

  1. University of Central Florida, USA

    K. Vajravelu

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© 2001 Kluwer Academic Publishers

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Puttaswamy, T.K. (2001). Global Behavior of Solutions of a Certain Nth Order Differential Equation in the Vicinity of an Irregular Singular Point. In: Vajravelu, K. (eds) Differential Equations and Nonlinear Mechanics. Mathematics and Its Applications, vol 528. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0277-3_19

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  • DOI: https://doi.org/10.1007/978-1-4613-0277-3_19

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-6867-0

  • Online ISBN: 978-1-4613-0277-3

  • eBook Packages: Springer Book Archive

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