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Differential equations singular in the solution variable

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Existence Theory for Nonlinear Ordinary Differential Equations

Part of the book series: Mathematics and Its Applications ((MAIA,volume 398))

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Abstract

This chapter discusses the second order differential equation y″ = f (t, y). Here f is not a Carathéodory function due to the singular behavior of its y variable and also the singular behavior of its t variable. Many physical situations are modelled by problems of this kind, for example problems in gas and fluid dynamics [3,7]. Several problems in nonlinear mechanics [7] lead to the second order boundary value problem

$$\left\{ {\begin{array}{*{20}{c}} {y'' + q\left( t \right){y^{ - \alpha }} = 0,0 < t < 1} \\ {y\left( 0 \right) = 0 = y\left( 1 \right).} \end{array}} \right.$$
(1.1)

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Authors and Affiliations

  1. Department of Mathematics, University College Galway, Galway, Ireland

    Donal O’Regan

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  1. Donal O’Regan
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© 1997 Springer Science+Business Media Dordrecht

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O’Regan, D. (1997). Differential equations singular in the solution variable. In: Existence Theory for Nonlinear Ordinary Differential Equations. Mathematics and Its Applications, vol 398. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1517-1_9

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  • DOI: https://doi.org/10.1007/978-94-017-1517-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4835-6

  • Online ISBN: 978-94-017-1517-1

  • eBook Packages: Springer Book Archive

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