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Positive solutions of semilinear elliptic boundary value problems

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Book cover Topological Methods in Differential Equations and Inclusions

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

Abstract

The paper is concerned with existence questions for positive solutions (ground states) of boundary value problems for semilinear elliptic partial differential equations. Global continuation and bifurcation results are used to obtain the existence of unbounded solution continua whenever the nonlinear terms depend upon a real parameter. Results are presented for various classes of nonlinear terms which are classified depending on their asymptotic growth, such as linear, superlinear, subcritical, and supercritical growth. Results describing the influence of the geometry, topology and dimension of the domain on the solution structure are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Utah, 84112, Salt Lake City, UT, USA

    Klaus Schmitt

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  1. Klaus Schmitt
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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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Schmitt, K. (1995). Positive solutions of semilinear elliptic boundary value problems. 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_10

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  • DOI: https://doi.org/10.1007/978-94-011-0339-8_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4150-8

  • Online ISBN: 978-94-011-0339-8

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