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Concentration of Solutions for Some Singularly Perturbed Neumann Problems

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1977)

Abstract

The purpose of these notes is to present some techniques for constructing solutions to a class of singularly perturbed problems with a precise asymptotic behavior when the perturbation parameter ε tends to zero. We first treat the case of concentration at points, and then the case of concentration at manifolds. One of the main motivations for the study of these equations arises from reaction-diffusion systems, concerning in particular the so-called Turing’s instability.

Keywords

  • Neumann Problem
  • Morse Index
  • Critical Point Theory
  • Smooth Bounded Domain
  • Critical Manifold

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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Malchiodi, A. (2009). Concentration of Solutions for Some Singularly Perturbed Neumann Problems. In: Chang, SY., Ambrosetti, A., Malchiodi, A. (eds) Geometric Analysis and PDEs. Lecture Notes in Mathematics(), vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01674-5_3

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