Skip to main content

Ambrosetti-Prodi type results in nonlinear boundary value problems

  • Conference paper
  • First Online:
Book cover Differential Equations and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. H. AMANN and P. HESS, A multiplicity result for a class of elliptic boundary value problems, Proc. R. Soc. Edinburgh 84A (1979) 145–151.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. AMBROSETTI and G. PRODI, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl. (4) 93 (1972) 231–247.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. BERESTYCKI and P.L. LIONS, Sharp existence results for a class of semilinear elliptic problems, Bol. Soc. Brasil. Mat. 12 (1981) 9–20.

    Article  MathSciNet  MATH  Google Scholar 

  4. M.S. BERGER and E. PODOLAK, On the solutions of a nonlinear Dirichlet problem, Indiana Univ. Math. J. 24 (1975) 837–846.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. BRÜLL and J. MAWHIN, Finiteness of the set of solutions of some boundary-value problems for ordinary differential equations, Sémin. Math. U.C.L. (NS) no 79, 1986.

    Google Scholar 

  6. K.C. CHANG, Variational methods and sub-and super-solutions, Scientia Sinica A-26 (1983) 1256–1265.

    MATH  Google Scholar 

  7. R. CHIAPPINELLI, J. MAWHIN and R. NUGARI, Generalized Ambrosetti-Prodi conditions for nonlinear two-point boundary value problems, preprint, 1986.

    Google Scholar 

  8. E.N. DANCER, On the ranges of certain weakly nonlinear elliptic partial differential equations, J. Math. Pures Appl. 57 (1978) 351–366.

    MathSciNet  MATH  Google Scholar 

  9. D.G. DE FIGUEIREDO, Lectures on boundary value problems of the Ambrosetti-Prodi type, in "Atas 12e Semin. Brasileiro Analise, Sao Paulo, 1980", 230–291.

    Google Scholar 

  10. D.G. DE FIGUEIREDO, On the superlinear Ambrosetti-Prodi problem, J. Nonlinear Analysis 8 (1984) 655–666.

    Article  MathSciNet  MATH  Google Scholar 

  11. D.G. DE FIGUEIREDO and S. SOLIMINI, A variational approach to superlinear elliptic problems, Comm. Partial Differential Equations 9 (1984) 699–717.

    Article  MathSciNet  MATH  Google Scholar 

  12. S.H. DING and J. MAWHIN, A multiplicity result for periodic solutions of higher-order ordinary differential equations, preprint, 1986.

    Google Scholar 

  13. C. FABRY, J. MAWHIN and M. NKASHAMA, A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London Math. Soc. 18 (1986) 173–180.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. GILBARG and N.S. TRUDINGER, "Elliptic Partial Differential Equations of Second Order", Second Edition, Springer, Berlin, 1983.

    Book  MATH  Google Scholar 

  15. R. KANNAN and R. ORTEGA, Superlinear elliptic boundary value problems, Czech. Math. J., to appear.

    Google Scholar 

  16. J.L. KAZDAN and F.W. WARNER, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (1975) 567–597.

    Article  MathSciNet  MATH  Google Scholar 

  17. H.W. KNOBLOCH, An existence theorem for periodic solutions of nonlinear ordinary differential equations, Michigan Math. J. 9 (1962) 303–309.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. MAWHIN, Recent results on periodic solutions of differential equations in "Intern. Conf. on Differential Equations", Academic Press, New York, 1975, 537–556.

    Google Scholar 

  19. J. MAWHIN, Boundary value problems with nonlinearities having infinite jumps, Comment. Math. Univ. Carolinae 25 (1984) 401–414.

    MathSciNet  MATH  Google Scholar 

  20. J. MAWHIN, "Points fixes, points critiques et problèmes aux limites", Sém. Math. Sup. no 92, Presses Univ. Montréal, 1985.

    Google Scholar 

  21. J. MAWHIN, First order ordinary differential equations with several periodic solutions, to appear.

    Google Scholar 

  22. M. NKASHAMA, A generalized upper and lower solutions method and multiplicity results for periodic solutions of nonlinear first order ordinary differential equations, preprint, 1986.

    Google Scholar 

  23. J.C. SCOVEL, Geometry of some nonlinear differential operators, Ph. D. Thesis, Courant Inst. New York University, 1983.

    Google Scholar 

  24. G. VIDOSSICH, Toward a theory for periodic solutions to first order differential equations, SISSA Trieste Report no 59/83/M, 1983.

    Google Scholar 

  25. J.R. WARD, Perturbations with some superlinear growth for a class of second order elliptic boundary value problems, J. Nonlinear Anal. 6 (1982) 367–374.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ian W. Knowles Yoshimi Saitō

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Mawhin, J. (1987). Ambrosetti-Prodi type results in nonlinear boundary value problems. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080609

Download citation

  • DOI: https://doi.org/10.1007/BFb0080609

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics