| 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:
|
http://hdl.handle.net/10338.dmlcz/126136 |
| . |
| 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:
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[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 |
| . |
