Previous |  Up |  Next


Title: The Hopf bifurcation theorem for parabolic equations with infinite delay (English)
Author: Petzeltová, Hana
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 116
Issue: 2
Year: 1991
Pages: 181-190
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Hopf bifurcation
Keyword: parabolic functional equation
Keyword: infinite delay
Keyword: singular kernel
MSC: 34K15
MSC: 34K30
MSC: 35B10
MSC: 35B32
MSC: 35R10
MSC: 45K05
MSC: 47N20
idZBL: Zbl 0749.35007
idMR: MR1112003
DOI: 10.21136/MB.1991.126136
Date available: 2009-09-24T20:44:53Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] M. G. Crandall P. H. Rabinowitz: Bifurcation, perturbation of simple eigenvalues and linearized stability.Arch. Rat. Mech. Anal. 52 (1973), 161-180. MR 0341212, 10.1007/BF00282325
Reference: [2] M. G. Crandall P. H. Rabinowitz: The Hopf bifurcation theorem in infinite dimensions.Aгch. Rat. Mech. Anal. 67 (1977), 53-72. MR 0467844, 10.1007/BF00280827
Reference: [3] J. M. Cushing: Integrodifferential equations and delay models in population dynamics.Lectuгe Notes in Biomath. Vol. 20, Springer-Verlag Berlin 1977. Zbl 0363.92014, MR 0496838, 10.1007/978-3-642-93073-7
Reference: [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). MR 0891773
Reference: [5] J. K. Hale: Theory of functional differential equations.Springer-Verlag, New York 1977. Zbl 0352.34001, MR 0508721
Reference: [б] D. Henry: Geometric theory of semilinear parabolic equations.Springer-Verlag Berlin-Heidelbeгg-New York 1981. Zbl 0456.35001, MR 0610244
Reference: [7] H. C. Simpson: Stability of periodic solutions of nonlinear integrodifferential systems.SIAM Ј. Appl. Math. 38 (1980), З41-З6З. Zbl 0457.45005, MR 0579423
Reference: [8] E. Sinestrari: On the abstract Cauchy problem in spaces of continuous functions.Ј. Math. Anal. Appl. 107 (1985), 16-66. MR 0786012, 10.1016/0022-247X(85)90353-1
Reference: [9] O. J. Staffans: Hopf bifurcation for an infinite delay functional equations.NATO ASI Series. Vol F 37, Springer-Verlag Berlin-Heidelberg 1987. MR 0921919
Reference: [10] H. W. Stech: Hopf bifurcation calculations for functional differential equations.Ј. Math. Anal. Appl. 109 (1985), 472-491. Zbl 0592.34048, MR 0802908, 10.1016/0022-247X(85)90163-5
Reference: [11] A. Tesei: Stability properties for partial Volterra integrodifferential equations.Аnn. Mat. Puгa Аppl. 126 (1980), 103-115. Zbl 0463.45009, MR 0612355
Reference: [12] A. Torchinski: Real-variable methods in harmonic analysis.Аcademic Press INC, 1986. MR 0869816
Reference: [13] Y. Yamada Y. Niikura: Bifurcation of periodic solutions for nonlinear parabolic equations with infinite delays.Funkc. Ekvac. 29 (1986), 309- ЗЗЗ. MR 0904545
Reference: [14] K. Yoshida: The Hopf bifurcation and its stability for semilinear diffusion equation with time delay arising in ecology.Hiгoshima Math. Ј. 12 (1982), 321-348. MR 0665499, 10.32917/hmj/1206133754
Reference: [15] K. Yoshida, K Kishimoto: Effect of two time delays on partially functional differential equations.Kumamoto Ј. Sci. (Math.) 15 (1983), 91-109. Zbl 0572.35086, MR 0705720


Files Size Format View
MathBohem_116-1991-2_8.pdf 1.437Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo