Annali di Matematica Pura ed Applicata

, Volume 120, Issue 1, pp 113–137 | Cite as

Critical point theory and the number of solutions of a nonlinear dirichlet problem

  • Alfonso Castro
  • A. C. Lazer


Dirichlet Problem Point Theory Critical Point Theory Nonlinear Dirichlet Problem 
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]
    S. Agmon -A. Douglis -L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math.,42 (1959), pp. 623–727.MathSciNetGoogle Scholar
  2. [2]
    A. Ambrosetti -G. Prodi,Ont he inversion of some differentiable mappings with singularities between Banach spaces, Annali Mat. Pura Appl.,93 (1972), pp. 231–246.MathSciNetGoogle Scholar
  3. [3]
    S. Bancroft -J. K. Hale -D. Sweet,Alternative problems and nonlinear functional equations, J. Diff. Egns.,4 (1968), pp. 40–56.CrossRefMathSciNetGoogle Scholar
  4. [4]
    L. Bers -F. John -M. Schechter,Partial differential equations, Interscience, New York, 1964.Google Scholar
  5. [5]
    A. Castro -A. Lazer,Applications of a max-min principle, Rev. Colombiana Mat.,4 h (1976), pp. 141–149.MathSciNetGoogle Scholar
  6. [6]
    L. Cesari,Functional analysis and Gelerkin's method, Mich. Math. J.,44 (1964), pp. 385–418.MathSciNetGoogle Scholar
  7. [7]
    N. Chow -J. Hale -J. Mallet-Paret,Applications of generic bifurcation, I, Arch. Rat. Mech. Anal.,2 (1975), pp. 159–188.MathSciNetGoogle Scholar
  8. [8]
    D. Clark,A variant of the Lusternik-Schnirelman theory, Indiana Univ. Math. J.,22 (1972), pp. 65–74.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    R. Courant -D. Hilbert,Methods of mathematical physics, vol. I, Interscience, New York, 1953.Google Scholar
  10. [10]
    R. Courant -D. Hilbert,Methods of mathematical physics, vol. 2, Interscience, New York, 1962.Google Scholar
  11. [11]
    C. Dolph,Nonlinear integral equations of the Hammerstein type, Trans. Amer. Math. Soc.,66 (1949), pp. 289–307.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    M. Greenberg,Lectures on algebraic topology, W. A. Benjamin, Inc., Reading, Mass., 1967.Google Scholar
  13. [13]
    J. Kazdan -F. Warner,Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.,28 (1975), pp. 567–597.MathSciNetGoogle Scholar
  14. [14]
    E. Landesman -A. Lazer,Linear eigenvalues and a nonlinear boundary value problem, Pacific J. of Math.,33 (1970), pp. 311–328.MathSciNetGoogle Scholar
  15. [15]
    S. Lang,Differential Manifolds, Addison-Wesley, Reading, Mass., 1972.Google Scholar
  16. [16]
    A. Lazer -E. Landesman -D. Meyers,On saddle point problems in the calculus of variations, the Ritz algorithm, and monotone convergence, J. Math. Anal. Appl.,53 (1975), pp. 594–614.CrossRefMathSciNetGoogle Scholar
  17. [17]
    J. Milnor,Topology from the differentiable viewpoint, University Press of Virginia, Charlottesville, 1965.Google Scholar
  18. [18]
    C. Miranda,Partial differential equations of elliptic type, Springer-Verlag, New York, Heidelberg, Berlin, 1970.Google Scholar
  19. [19]
    C. Morrey,Multiple integrals in the calculus of variations, Springer, New York, 1966.Google Scholar
  20. [20]
    P. Rabinowitz,A note on topological degree for potential operators, J. Math. Anal. Appl.,51 (1975), pp. 483–492.CrossRefMATHMathSciNetGoogle Scholar
  21. [21]
    E. Rothe,A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors, Math. Nacht.,4 (1950–51), pp. 12–27.MathSciNetGoogle Scholar
  22. [22]
    E. Spanier,Algebraic topology, McGraw-Hill, New York, 1966.Google Scholar
  23. [23]
    M. Vainberg,Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1979

Authors and Affiliations

  • Alfonso Castro
    • 1
  • A. C. Lazer
    • 2
  1. 1.Mexico D. F.Mexico
  2. 2.Cincinnati

Personalised recommendations