The Hopf bifurcation theorem for parabolic equations with infinite delay

Hana Petzeltová

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 2, page 181-190
  • ISSN: 0862-7959

Abstract

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The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.

How to cite

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Petzeltová, Hana. "The Hopf bifurcation theorem for parabolic equations with infinite delay." Mathematica Bohemica 116.2 (1991): 181-190. <http://eudml.org/doc/29290>.

@article{Petzeltová1991,
abstract = {The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.},
author = {Petzeltová, Hana},
journal = {Mathematica Bohemica},
keywords = {Hopf bifurcation; parabolic functional equation; infinite delay; singular kernel; singular kernel},
language = {eng},
number = {2},
pages = {181-190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Hopf bifurcation theorem for parabolic equations with infinite delay},
url = {http://eudml.org/doc/29290},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Petzeltová, Hana
TI - The Hopf bifurcation theorem for parabolic equations with infinite delay
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 2
SP - 181
EP - 190
AB - The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
LA - eng
KW - Hopf bifurcation; parabolic functional equation; infinite delay; singular kernel; singular kernel
UR - http://eudml.org/doc/29290
ER -

References

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  3. J. M. Cushing, 10.1007/978-3-642-93073-7, Lectuгe Notes in Biomath. Vol. 20, Springer-Verlag Berlin 1977. (1977) Zbl0363.92014MR0496838DOI10.1007/978-3-642-93073-7
  4. G. Da Prato A. Lunardi, Hopf bifurcation for nonlinear integrodifferential equations in Banach spaces with infinite delay, Indiana Univ. Math. Ј., Vol. 36, No 2 (1987). (1987) MR0891773
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  8. E. Sinestrari, 10.1016/0022-247X(85)90353-1, Ј. Math. Anal. Appl. 107 (1985), 16-66. (1985) MR0786012DOI10.1016/0022-247X(85)90353-1
  9. O. J. Staffans, Hopf bifurcation for an infinite delay functional equations, NATO ASI Series. Vol F 37, Springer-Verlag Berlin-Heidelberg 1987. (1987) MR0921919
  10. H. W. Stech, 10.1016/0022-247X(85)90163-5, Ј. Math. Anal. Appl. 109 (1985), 472-491. (1985) Zbl0592.34048MR0802908DOI10.1016/0022-247X(85)90163-5
  11. A. Tesei, Stability properties for partial Volterra integrodifferential equations, Аnn. Mat. Puгa Аppl. 126 (1980), 103-115. (1980) Zbl0463.45009MR0612355
  12. A. Torchinski, Real-variable methods in harmonic analysis, Аcademic Press INC, 1986. (1986) MR0869816
  13. Y. Yamada Y. Niikura, Bifurcation of periodic solutions for nonlinear parabolic equations with infinite delays, Funkc. Ekvac. 29 (1986), 309- ЗЗЗ. (1986) MR0904545
  14. K. Yoshida, 10.32917/hmj/1206133754, Hiгoshima Math. Ј. 12 (1982), 321-348. (1982) MR0665499DOI10.32917/hmj/1206133754
  15. K. Yoshida, K Kishimoto, Effect of two time delays on partially functional differential equations, Kumamoto Ј. Sci. (Math.) 15 (1983), 91-109. (1983) Zbl0572.35086MR0705720

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