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On positive solutions of semilinear periodic-parabolic problems

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References

  1. Amann, H.: Periodic solutions of semilinear parabolic equations. In: Nonlinear Analysis, ed. Cesari-Kannan-Weinberger, Academic Press 1978, p. 1–29.

    Google Scholar 

  2. Beltramo, A.: Publication to appear.

    Google Scholar 

  3. Beltramo, A., P. Hess: On the principal eigenvalue of a periodic-parabolic operator, Preprint.

    Google Scholar 

  4. Castro A., A.C. Lazer: Results on periodic solutions of parabolic equations suggested by elliptic theory, Bull. U.M.I. (6) 1-B (1982), 1089–1104.

    MathSciNet  MATH  Google Scholar 

  5. Crandall, M.G., P.H. Rabinowitz: Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rat. Mech. Anal. 52 (1973), 161–180.

    Article  MathSciNet  MATH  Google Scholar 

  6. de Figueiredo, D.G.: Positive solutions of semilinear elliptic problems, Course Latin-American school of differential equations, Sao Paulo, June 1981.

    Google Scholar 

  7. Gossez, J.P., E. Lami Dozo: On the principal eigenvalue of a second order linear elliptic problem, Arch. Rat. Mech. Anal., to appear.

    Google Scholar 

  8. Gossez, J.P., E. Lami Dozo: On an estimate for the principal eigenvalue of a linear elliptic problem, to appear in Portug. Math.

    Google Scholar 

  9. Hess, P.: On bifurcation and stability of positive solutions of nonlinear elliptic eigenvalue problems. In: Dynamical Systems II, ed. Bednarek-Cesari, Academic Press 1982, p. 103–119.

    Google Scholar 

  10. Hess, P.: On the principal eigenvalue of a second order linear elliptic problem with an indefinite weight function, Math. Z. 179 (1982), 237–239.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hess, P., T. Kato: On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. P.D.E. 5 (1980), 999–1030.

    Article  MathSciNet  MATH  Google Scholar 

  12. Holland, C.J.: A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions, Comm. P.A.M. 31 (1978), 509–519.

    MathSciNet  MATH  Google Scholar 

  13. Kato, T.: Superconvexity of the spectral radius, and convexity of the spectral bound and type, Math. Z. 180 (1982), 265–273.

    Article  MathSciNet  MATH  Google Scholar 

  14. Kolesov, Ju.S.: A test for the existence of periodic solutions to parabolic equations, Soviet Math. Dokl. 7 (1966), 1318–1320.

    MATH  Google Scholar 

  15. Krein, M.G., M.A. Rutman: Linear operators leaving invariant a cone in a Banach space, Amer. Math. Soc. Transl. 10 (1962), 199–325.

    MathSciNet  MATH  Google Scholar 

  16. Lazer, A.C.: Some remarks on periodic solutions of parabolic differential equations. In: Dynamical Systems II, ed. Bednarek-Cesari, Academic Press 1982, p. 227–246.

    Google Scholar 

  17. Protter, M.H., H.F. Weinberger: Maximum Principles in Differential Equations. Prentice Hall 1967.

    Google Scholar 

  18. Tanabe, H.: Equations of evolution, Pitman 1979.

    Google Scholar 

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Franz Kappel Wilhelm Schappacher

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© 1984 Springer-Verlag

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Hess, P. (1984). On positive solutions of semilinear periodic-parabolic problems. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072770

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  • DOI: https://doi.org/10.1007/BFb0072770

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

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