| Title:
|
New results on periodic solutions for a kind of Rayleigh equation (English) |
| Author:
|
Tang, Mei-Lan |
| Author:
|
Liu, Xin-Ge |
| Author:
|
Liu, Xin-Bi |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
79-85 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the existence of periodic solutions for a kind of non-autonomous time-delay Rayleigh equation. With the continuation theorem of the coincidence degree and a priori estimates, some new results on the existence of periodic solutions for this kind of Rayleigh equation are established. (English) |
| Keyword:
|
Rayleigh equations |
| Keyword:
|
existence |
| Keyword:
|
periodic solution |
| Keyword:
|
a priori estimate |
| MSC:
|
34C25 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1212.34124 |
| idMR:
|
MR2476023 |
| DOI:
|
10.1007/s10492-009-0006-8 |
| . |
| Date available:
|
2010-07-20T12:48:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140351 |
| . |
| Reference:
|
[1] Chen, F. D.: Existence and uniqueness of almost periodic solutions for forced Rayleigh equations.Ann. Differ. Equations 17 (2001), 1-9. MR 1829382 |
| Reference:
|
[2] Chen, F. D., Chen, X. X., Lin, F. X., Shi, J. L.: Periodic solution and global attractivity of a class of differential equations with delays.Acta Math. Appl. Sin. 28 (2005), 55-64 Chinese. MR 2157759 |
| Reference:
|
[3] Deimling, K.: Nonlinear Functional Analysis.Springer Berlin (1985). Zbl 0559.47040 |
| Reference:
|
[4] Gaines, R. E., Mawhin, J. L.: Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics, Vol. 568.Springer Berlin (1977). 10.1007/BFb0089537 |
| Reference:
|
[5] Huang, C., He, Y., Huang, L., Tan, W.: New results on the periodic solutions for a kind of Reyleigh equation with two deviating arguments.Math. Comput. Modelling 46 (2007), 604-611. MR 2329595, 10.1016/j.mcm.2006.11.024 |
| Reference:
|
[6] Liu, F.: On the existence of the periodic solutions of Rayleigh equation.Acta Math. Sin. 37 (1994), 639-644 Chinese. Zbl 0812.34037 |
| Reference:
|
[7] Lu, S. P., Ge, W. G.: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument.Nonlinear Anal., Theory Methods Appl. 56 (2004), 501-514. Zbl 1078.34048, MR 2035324 |
| Reference:
|
[8] Lu, S. P., Ge, W. G., Zheng, Z. X.: Periodic solutions for a kind of Rayleigh equation with a deviating argument.Appl. Math. Lett. 17 (2004), 443-449. Zbl 1073.34081, MR 2045750, 10.1016/S0893-9659(04)90087-0 |
| Reference:
|
[9] Lu, S. P., Ge, W. G., Zheng, Z. X.: Periodic solutions for a kind of Rayleigh equation with a deviating argument.Acta Math. Sin. 47 (2004), 299-304. Zbl 1073.34081, MR 2074353 |
| Reference:
|
[10] Peng, L.: Periodic solutions for a kind of Rayleigh equation with two deviating arguments.J. Franklin Inst. 7 (2006), 676-687. Zbl 1114.34051, MR 2293410, 10.1016/j.jfranklin.2006.04.001 |
| Reference:
|
[11] Wang, G.-Q., Cheng, S. S.: A priori bounds for periodic solutions of a delay Rayleigh equation.Appl. Math. Lett. 12 (1999), 41-44. Zbl 0980.34068, 10.1016/S0893-9659(98)00169-4 |
| Reference:
|
[12] Wang, G.-Q., Yan, J. R.: Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type.Portugal. Math. 57 (2000), 153-160. Zbl 0963.34069 |
| Reference:
|
[13] Wang, G.-Q., Yan, J. R.: On existence of periodic solutions of the Rayleigh equation of retarded type.Int. J. Math. Math. Sci. 23 (2000), 65-68. Zbl 0949.34059, 10.1155/S0161171200001836 |
| Reference:
|
[14] Zhou, Y., Tang, X.: On existence of periodic solutions of Rayleigh equation of retarded type.J. Comput. Appl. Math. 203 (2007), 1-5. Zbl 1115.34067, MR 2313817, 10.1016/j.cam.2006.03.002 |
| . |
