Hopf bifurcation for fully nonlinear equations in Banach space

Giuseppe Da Prato; Alessandra Lunardi

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 4, page 315-329
  • ISSN: 0294-1449

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Da Prato, Giuseppe, and Lunardi, Alessandra. "Hopf bifurcation for fully nonlinear equations in Banach space." Annales de l'I.H.P. Analyse non linéaire 3.4 (1986): 315-329. <http://eudml.org/doc/78116>.

@article{DaPrato1986,
author = {Da Prato, Giuseppe, Lunardi, Alessandra},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear evolution equations; first order differential equation; Hopf bifurcation; spectral properties},
language = {eng},
number = {4},
pages = {315-329},
publisher = {Gauthier-Villars},
title = {Hopf bifurcation for fully nonlinear equations in Banach space},
url = {http://eudml.org/doc/78116},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Da Prato, Giuseppe
AU - Lunardi, Alessandra
TI - Hopf bifurcation for fully nonlinear equations in Banach space
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 4
SP - 315
EP - 329
LA - eng
KW - nonlinear evolution equations; first order differential equation; Hopf bifurcation; spectral properties
UR - http://eudml.org/doc/78116
ER -

References

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  2. [2] M.G. Crandall, P.H. Rabinowitz, The Hopf bifurcation theorem in infinite dimensions, Arch. Rat. Mech. Anal., t. 68, 1978, p. 53-72. Zbl0385.34020MR467844
  3. [3] G. Da Prato, P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Maths. Pures Appl., t. 54, 1975, p. 305-387. Zbl0315.47009MR442749
  4. [4] J.K. Hale, J. Scheurle, Smoothness of bounded solutions of nonlinear evolution equations, J. Diff. Eq., t. 56, 1985, p. 142-163. Zbl0505.34029MR772123
  5. [5] D. Henry, Geometric theory of semilinear parabolic equations, Lectures Notes in Mathematics, n° 840, Springer-Verlag, Berlin, 1981. Zbl0456.35001MR610244
  6. [6] G. Iooss, Bifurcation of maps and applications, Elsevier, North-Holland, New York, 1979. Zbl0408.58019MR531030
  7. [7] J. Ize, Periodic solutions of nonlinear parabolic equations, Comm. Part. Diff. Eq., t. 4, 1979. p. 1299-1387. Zbl0436.35012MR551656
  8. [8] H. Kielhöfer, Hopf bifurcation at multiple eigenvalues, Arch. Rat. Mech. Anal., t. 69, 1979, p. 53-83. Zbl0398.34058MR513959
  9. [9] H. Kielhöfer, Generalized Hopf bifurcation in Hilbert space, Math. Meth. in the Appl. Sci., t. 1, 1979, p. 498-513. Zbl0451.34059MR548684
  10. [10] J.L. Lions, J. Peetre, Sur une classe d'espaces d'interpolation, Publ. I. H. E. S., Paris, t. 19, 1964, p. 5-68. Zbl0148.11403MR165343
  11. [11] J. Marsden, M.F. Mccracken, The Hopf bifurcation and its applications, Springer-Verlag, Berlin, 1976. Zbl0346.58007MR494309
  12. [12] P. Negrini, A. Tesei, Attractivity and Hopf bifurcation in Banach spaces. J. Math. An. Appl., t. 78, 1980, p. 204-221. Zbl0452.35050MR595777
  13. [13] D.H. Sattinger, Topics in stability and bifurcation theory, Springer-Verlag, Berlin, 1973. Zbl0248.35003MR463624
  14. [14] E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. An. Appl., t. 107, 1985, p. 16-66. Zbl0589.47042MR786012

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