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A Note on the Superlinear Ambrosetti-Prodi Type Problem in a Ball

  • P.N. Srikanth
  • Sanjiban Santra
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 66)

Abstract

Using a careful analysis of the Morse indices of the solutions obtained by using the Mountain Pass Theorem applied to the associated Euler- Lagrange functional acting both on the full space H 0 1 (Ω) and on its subspace H 0,r 1 (Ω) of radially symmetric functions we prove the existence of non-radially symmetric solutions of a problem of Ambrosetti-Prodi type in a ball.

Keywords

Mountain Pass Theorem non-radial solutions Morse index concentration 

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References

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    E.N. Dancer and Yan Shusen, Multiplicity and Profile of the changing sign solutions for an Elliptic Problem of Ambrosetti-Prodi type, preprint.Google Scholar
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    D.G. deFigueiredo, P.N. Srikanth and Santra Sanjiban, Non-radially Symmetric Solutions for a Superlinear Ambrosetti-Prodi Type Problem in a Ball, Communications in Contemporary Mathematics, to appear.Google Scholar
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    I. Ekeland and N. Ghoussoub, Selected new aspects of the calculus of variation in the large, Bull. of the AMS 39 (2002), 207–265.zbMATHCrossRefMathSciNetGoogle Scholar
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    N. Ghoussoub, Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Mathematics, 107, Cambridge University Press.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • P.N. Srikanth
    • 1
  • Sanjiban Santra
    • 2
  1. 1.TIFR CentreIISc CampusBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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