Compression–Expansion Critical Point Theorems in Conical Shells

  • Radu Precup
Part of the Springer Optimization and Its Applications book series (SOIA, volume 35)


We present compression and expansion type critical point theorems in a conical shell of a Hilbert space identified to its dual. The notion of linking is involved and the compression–expansion boundary conditions are expressed with respect to only one norm.


Hilbert Space Complementarity Problem Convergent Subsequence Conical Shell Mountain Pass 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    V. Benci, Some critical point theorems and applications, Comm. Pure Appl. Math. 33 (1980), 147-172.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    K. Deimling, Ordinary Differential Equations in Banach Spaces, Springer, Berlin, 1977.MATHGoogle Scholar
  4. 4.
    K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.MATHGoogle Scholar
  5. 5.
    M. Frigon, On a new notion of linking and application to elliptic problems at resonance, J. Differential Equations 153 (1999), 96-120.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, 2003.MATHGoogle Scholar
  7. 7.
    G. Isac, Leray-Schauder Type Alternatives, Complementarity Problems and Variational Inequalities, Kluwer, Dordrecht, 2006.MATHGoogle Scholar
  8. 8.
    M.A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.Google Scholar
  9. 9.
    D. O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.MATHGoogle Scholar
  10. 10.
    R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.MATHGoogle Scholar
  11. 11.
    R. Precup, A compression type mountain pass theorem in conical shells, J. Math. Anal. Appl. 338 (2008), 1116-1130.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    R. Precup, The Leray-Schauder boundary condition in critical point theory, Nonlinear Anal., 71(2009), 3218–3228.Google Scholar
  13. 13.
    M. Schechter, Linking Methods in Critical Point Theory, Birkhäuser, Basel, 1999.MATHGoogle Scholar
  14. 14.
    M. Struwe, Variational Methods, Springer, Berlin, 1990.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsBabeş–Bolyai UniversityClujRomania

Personalised recommendations