Skip to main content

Reduction methods via minimax

  • Conference paper
  • First Online:
Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 957))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Adams, Sobolev Spaces, Academic Press, New York, San Francisco, London (1975).

    MATH  Google Scholar 

  2. S. Ahmad, A.C. Lazer and J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933–944.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Amann, Saddle points and multiple solutions of differential equations, Math. Z. (1979), 127–166.

    Google Scholar 

  4. A. Ambrosetti, and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Annali Math. Pura Appl., 93 (1972) 231–247.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Bates and A. Castro, Existence and uniqueness for a variational hyperoblic system without resonance, Nonlinear Analysis, Theory, Methods and Applications, 4 (1980), 1151–1156.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Bates and A. Castro, Necessary and sufficient conditions fon existence of solutions to equations with noninvertible linear part, to appear in volume XV (numbers 1–2) of the Revista Colombiana de Matemáticas.

    Google Scholar 

  7. A. Castro, Hammerstein integral equations with indefinite Kernel, Internat. J. Math. and Math. Sci., 1 (1978), 187–201.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Castro, A two point boundary value problem with jumping nonlinearities, Proc. Amer. Math. Soc., 79 (1980), 207–211.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Castro, Periodic solutions of the forced pendulum equation, Differential Equations, Editors S. Ahmad, M. Keener and A.C. Lazer, Academic Press (1980), 149–160.

    Google Scholar 

  10. A. Castro, Existence of infinitely many solutions for a class of superlinear problems, (preprint).

    Google Scholar 

  11. A. Castro, Métodos variacionales y análisis functional no lineal, edited by the Universidad Pedagógica y Tecnológ ca de Colombia and the Sociedad Colombiana de Matemáticas (1980).

    Google Scholar 

  12. A. Castro and A. C. Lazer, Applications of a maxmin principle, Rev. Colombiana Mat., 10 (1976), 141–149.

    MathSciNet  MATH  Google Scholar 

  13. A. Castro and A. C. Lazer, Critical point theory and the number of solutions of a nonlinear Dirichlet problem. Annali Mat. Pura Appl., CXX (1979), 113–137.

    Article  MathSciNet  MATH  Google Scholar 

  14. E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic equations at resonance, J. Math. Mech., 19 (1970), 609–623.

    MathSciNet  MATH  Google Scholar 

  15. A. C. Lazer, E. M. Landesman and D. Meyers, On saddle point problems in the calculus of variations, the Ritz algorithm, and monotone convergence, J. Math. Anal. Appl., 52 (1975), 594–614.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. A. Lusternik and V. J. Sobolev, Functional analysis, Hindustan Publishing Corpn. (India), Delhi (1961).

    Google Scholar 

  17. L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. A. Math. Soc., 4 (1981), 267–302.

    Article  MathSciNet  MATH  Google Scholar 

  18. P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157–184.

    Article  MathSciNet  Google Scholar 

  19. H. L. Royden, Real analysis, McMillan Publishing Co., New York (1968).

    MATH  Google Scholar 

  20. M. Vainberg, Variational methods for the study of nonlinear operators, Holden Day, San Francisco (1964).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Djairo Guedes de Figueiredo Chaim Samuel Hönig

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Alfonso, C.B. (1982). Reduction methods via minimax. In: Guedes de Figueiredo, D., Hönig, C.S. (eds) Differential Equations. Lecture Notes in Mathematics, vol 957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066231

Download citation

  • DOI: https://doi.org/10.1007/BFb0066231

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11951-7

  • Online ISBN: 978-3-540-39539-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics