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On Indefinite Nonlinear Neumann Problems

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Partial Differential and Integral Equations

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 2))

Abstract

We study the subcritical nonlinear Neumann problem −Δu =a(x)u p in a bounded domain Ω ⊂ ℝn with boundary condition ∂n u = b(x)u q on ∂Ω, where a andb are continuous functions which may change sign. We derive existence and nonexistence results for positive solutions of this problem. In addition, we extend these results to a nonlinear interface problem in a domain \(\Omega = {\Omega _1} \cup {\Omega _2} \) with interface conditions = ∂n u 1 = ∂n u 2, b(x)∣u 1∣q−1 u 1 = λ(x)u 2 on \(\overline {{\Omega _1}} \cap \overline {{\Omega _2}} \).

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Author information

Authors and Affiliations

  1. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Klaus Pflüger

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  1. Klaus Pflüger
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Editor information

Editors and Affiliations

  1. Freie Universität Berlin, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, Delaware, USA

    Robert P. Gilbert

  3. Peking University, Beijing, China

    Guo-Chun Wen

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© 1999 Kluwer Academic Publishers

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Pflüger, K. (1999). On Indefinite Nonlinear Neumann Problems. In: Begehr, H.G.W., Gilbert, R.P., Wen, GC. (eds) Partial Differential and Integral Equations. International Society for Analysis, Applications and Computation, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3276-3_25

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  • DOI: https://doi.org/10.1007/978-1-4613-3276-3_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3278-7

  • Online ISBN: 978-1-4613-3276-3

  • eBook Packages: Springer Book Archive

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