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Positive solutions of semilinear elliptic problems

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Differential Equations

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

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References

  1. M. A. Krasnosels’kii, "Positive solutions of Operator equations". P. Noordhoff, Groningen (1964).

    Google Scholar 

  2. Herbert Amann, "Fixed point equation and nonlinear eigenvalue problems in ordered Banach spaces", S.I.A.M. Review 18 (1976), p. 620–709.

    MathSciNet  MATH  Google Scholar 

  3. Antonio Ambrosetti, "On exact number of positive solutions of convex nonlinear problems". Bolletino U.M.I. vol 15-A (1978) p. 610–615.

    MathSciNet  MATH  Google Scholar 

  4. Antonio Ambrosetti-Giovanni Mancini, "Sharp nonuniqueness results for some nonlinear problems". Nonlinear Analysis, Theory, Methods & Applications, vol. 3 (1979), p. 635–645.

    Article  MathSciNet  MATH  Google Scholar 

  5. Henri Berestycki, "Constributions à l’étude des problèmes aux limites elliptiques non-linéaires". Thèse de Doctorat d’État ès Sciences Mathématiques présentée à l’Université Pierre et Marie Curie, Paris (Février 1980).

    Google Scholar 

  6. Peter Hess-Tosio Kato, "On some linear and nonlinear eigenvalue problems with an indefinite weight function". Comm. P.D.E. 5 (1980) p. 999–1030.

    Article  MathSciNet  MATH  Google Scholar 

  7. Antonio Ambrosetti-Paul H. Rabinowitz, "Dual variational methods in critical point theory and applications", J. Functional Analysis 14 (1973), p. 369–381.

    Article  MathSciNet  MATH  Google Scholar 

  8. Haim Brezis-Robert E. L. Turner, "On a class of superlinear elliptic problems", Comm. in P.D.E., 2 (1977), p. 601–614.

    Article  MathSciNet  MATH  Google Scholar 

  9. Michael G. Crandall-Paul H. Rabinowitz, "Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems", Arch. Rat. Mech. Anal. 58 (1975), p. 207–218.

    Article  MathSciNet  MATH  Google Scholar 

  10. Roger D. Nussbaum, "Positive Solutions of nonlinear elliptic boundary value problems", J. Math. Anal. Appl. 51 (1975), p. 461–482.

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Mignot-Jean Pierre Puel, "Sur une classe de problèmes non linéaires avec nonlinearité positive, croissante, convexe". To appear.

    Google Scholar 

  12. Robert E. L. Turner, "A priori bounds for positive solutions of nonlinear elliptic equations in two variables", Duke Math. J. 41 (1974), p. 759–774.

    Article  MathSciNet  MATH  Google Scholar 

  13. Adele Manes-Ana Maria Micheletti, "Un’estensione della teoria variazionale classica degli autovalori per operatori ellittici del secondo ordine". Bolletino U.M.I. vol. 7 (1973) p. 285–301.

    MathSciNet  MATH  Google Scholar 

  14. Guido Stampacchia, "Equations Elliptiques du Second Ordre à Coefficients Discontinues". Les Presses de l’Université de Montréal (1966).

    Google Scholar 

  15. Guido Stampacchia, "Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus". Ann. Inst. Fourier 15 (1965), p. 189–258.

    Article  MathSciNet  MATH  Google Scholar 

  16. David Gilbarg-Neils S. Trudinger, "Elliptic Partial Differential Equations of Second Order". Springer-Verlag (1977).

    Google Scholar 

  17. Herbert Amann, "On the existence of positive solutions of nonlinear elliptic boundary value problems". Indiana Univ. Math. J. vol. 21 (1971), p. 125–146.

    Article  MathSciNet  MATH  Google Scholar 

  18. David H. Sattinger, "Monotone methods in nonlinear elliptic and parabolic boundary value problems". Indiana Univ. Math. J. vol. 21 (1972), pp. 979–1000.

    Article  MathSciNet  MATH  Google Scholar 

  19. David H. Sattinger, "Topics in Stability and Bifurcation Theory". Lecture Notes vol. 309, Springer Verlag (1973).

    Google Scholar 

  20. Antonio Ambrosetti-Peter Hess, "Positive solutions of Asymptotically Linear Elliptic Eigenvalue Problems". Journal of Math. Anal. Appl. vol 73 (1980), pp. 411–422.

    Article  MathSciNet  MATH  Google Scholar 

  21. Melvyn S. Berger, "Nonlinear Problems with exactly three solutions". Indiana University Mathematics Journal. Vol 28 (1979), p. 689–698.

    Article  MathSciNet  MATH  Google Scholar 

  22. Alan C. Lazer-P. J. McKenna, "On multiple solutions of a nonlinear Dirichlet problem". Differential Equations. Academic Press (1980) p. 199–214.

    Google Scholar 

  23. Djairo Guedes de Figueiredo, "Lectures on Boundary Value Problems of the Ambrosetti-Prodi type". Atas do 120 Seminário Brasileiro de Análise. São José dos Campos S.P. (Oct. 1980).

    Google Scholar 

  24. Henri Berestycki, "Méthodes Topologiques et Problèmes aux Limites non-linéaires". Université de Paris (1975).

    Google Scholar 

  25. James Dugundji, "An extension of Tietze’s theorem" Pacific J. Math. vol. 1 (1951), pp. 353–367.

    Article  MathSciNet  MATH  Google Scholar 

  26. G. H. Hardy-J. Littlewood-G. Polya, "Inequalities". Cambridge University Press.

    Google Scholar 

  27. J.-L. Lions-G. Magenes, "Nonhomogeneous Boundary Value Problems and Applications", Vol. 1. Springer, Berlin (1970).

    MATH  Google Scholar 

  28. Djairo Guedes de Figueiredo-Pierre-Louis Lions-Roger D. Nussbaum, "A priori estimates for positive solutions of semilinear elliptic equations". To appear.

    Google Scholar 

  29. S. I. Pohozaev, "Eigenfunctions of Δu+λf(u)=0", Soviet Math. Dokl. 6 (1965), p. 1408–1411.

    MathSciNet  Google Scholar 

  30. Basilis Gidas-Weiming Ni-Louis Nirenberg, "Symmetry and related properties via the maximum principle", Comm. Math. Phys. 68 (1979), p. 209–243.

    Article  MathSciNet  MATH  Google Scholar 

  31. O. Ladyzhenskaya-N. Uraltseva, "Linear and Quasilinear Elliptic Equations", translated by Scripta Technica, Academic Press, New York, 1968.

    Google Scholar 

  32. Basilis Gidas-Joel Spruck, "A priori bounds for positive solutions of nonlinear elliptic equations". Comm. P.D.E. vol 6 (1981) p. 883–901.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departmento de Matemática, Universidade de Brasília, Brasília, DF, Brazil

    Djairo Guedes de Figueiredo

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  1. Djairo Guedes de Figueiredo
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Djairo Guedes de Figueiredo Chaim Samuel Hönig

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© 1982 Springer-Verlag

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Guedes de Figueiredo, D. (1982). Positive solutions of semilinear elliptic problems. 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/BFb0066233

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  • DOI: https://doi.org/10.1007/BFb0066233

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11951-7

  • Online ISBN: 978-3-540-39539-3

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