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Annali di Matematica Pura ed Applicata

, Volume 148, Issue 1, pp 367–395 | Cite as

Coercive singular perturbations: Eigenvalue problems and bifurcation phenomena

  • L. S. Frank
Article

Summary

The method based upon a constructive reduction of coercive singular perturbations to regular ones, introduced in 1977 (see [4]) and developed later on (see [9–11]) is applied for computing the asymptotic expansions for eigenvalues of coercive singular perturbations, when the small parameter goes to zero. The same method turns out to be useful for investigating the asymptotic behaviour of solutions to quasi-linear coercive singular perturbations in the neighbourhood of the bifurcation points. It can be applied to classes of quasi-linear singular perturbations whose principal linear part in local representation is coercive and the nonlinear part is analytic in some ball in the solution space with values in the data space. The results are summarized in [7, 8].

Keywords

Asymptotic Behaviour Asymptotic Expansion Eigenvalue Problem Small Parameter Solution Space 
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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Copyright information

© Fondazione Annali di Matematica Pura ed Aplicata 1987

Authors and Affiliations

  • L. S. Frank
    • 1
  1. 1.Mathematische InstitutKatholieke UniversiteitED NijmegenNetherlands

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