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Existence principles for differential equations and systems of equations

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Topological Methods in Differential Equations and Inclusions

Part of the book series: NATO ASI Series ((ASIC,volume 472))

Abstract

These lectures cover basic existence and sometimes uniqueness principles for systems of ordinary differential equations and for equations in Banach spaces. The existence principles are established by means of topological methods based on nonlinear alternatives for compact maps and for contractive maps. The initial analysis treats both classical and Carathéodory problems on compact intervals simultaneously and in a classical setting by recasting the boundary value problem as an equivalent integro-differential equation. Later problems with more general singularities and/or unbounded intervals are treated.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97330, USA

    John W. Lee

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

    Donal O’Regan

Authors
  1. John W. Lee
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  2. Donal O’Regan
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Editor information

Editors and Affiliations

  1. Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, Canada

    Andrzej Granas , Marlène Frigon  & Gert Sabidussi ,  & 

  2. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Toruń, Poland

    Andrzej Granas

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Lee, J.W., O’Regan, D. (1995). Existence principles for differential equations and systems of equations. In: Granas, A., Frigon, M., Sabidussi, G. (eds) Topological Methods in Differential Equations and Inclusions. NATO ASI Series, vol 472. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0339-8_6

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  • DOI: https://doi.org/10.1007/978-94-011-0339-8_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4150-8

  • Online ISBN: 978-94-011-0339-8

  • eBook Packages: Springer Book Archive

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