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 


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