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Nonlinear Diffusion Equations and Their Equilibrium States II pp 217–233Cite as

A Survey of Some Superlinear Problems

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Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 13))

Abstract

Consider the semilinear elliptic partial differential equation:

$$ \left\{ {\begin{array}{*{20}{c}} { - \Delta u = p\left( {x,u} \right)} & {x \in \Omega } \\ {u = 0} & {x \in \partial \Omega } \\ \end{array} } \right. $$
(0.1)

Here and in what follows, Ω always denotes a bounded domain in ℝn with a smooth boundary. Suppose that p(x,ξ) is superlinear as |ξ| → ∞, i.e.

$$ p(x,\xi ){\xi ^{{ - 1}}} \to \infty \;as\;\left| \xi \right| \to \infty $$
((0.2))

.

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Author information

Authors and Affiliations

  1. Mathematics Department and Mathematics Research Center, University of Wisconsin, Madison, WI, 53706, USA

    Paul H. Rabinowitz

Authors
  1. Paul H. Rabinowitz
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    W.-M. Ni  & James Serrin  & 

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA, 94720, USA

    W.-M. Ni  & James Serrin  & 

  3. Department of Mathematics and Computer Science, University of Leiden, The Netherlands

    L. A. Peletier

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© 1988 Springer-Verlag New York Inc.

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Rabinowitz, P.H. (1988). A Survey of Some Superlinear Problems. In: Ni, WM., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States II. Mathematical Sciences Research Institute Publications, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9608-6_12

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  • DOI: https://doi.org/10.1007/978-1-4613-9608-6_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9610-9

  • Online ISBN: 978-1-4613-9608-6

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