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Semilinear Problems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1991)

Abstract

We study the elliptic polyharmonic reaction-diffusion-type model equation

$$ (-\Delta)^m u=f(u) $$

in bounded domains Ω⊂ℝn and in most cases together with Dirichlet boundary conditions

$$ D^\alpha u|_{\partial\Omega}\ = \ 0 \ for |\alpha| \leq m-1. $$

These boundary conditions prevent (7.1) from being written as a system of second order boundary value problems. However, in some cases, also (homogeneous) Navier boundary conditions (2.21) or Steklov boundary conditions (2.22) may be particularly interesting.

Keywords

  • Dirichlet Problem
  • Singular Solution
  • Radial Solution
  • Critical Growth
  • Nonexistence Result

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Filippo Gazzola .

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© 2010 Springer-Verlag Berlin Heidelberg

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Gazzola, F., Grunau, HC., Sweers, G. (2010). Semilinear Problems. In: Polyharmonic Boundary Value Problems. Lecture Notes in Mathematics(), vol 1991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12245-3_7

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