| Title:
|
On existence of positive periodic solutions of a kind of Rayleigh equation with a deviating argument (English) |
| Author:
|
Zhou, Yinggao |
| Author:
|
Wu, Min |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
189-196 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence of positive periodic solutions for a kind of Rayleigh equation with a deviating argument $$ x''(t)+ f(x'(t))+ g(t,x(t-\tau (t)))= p(t) $$ is studied. Using the coincidence degree theory, some sufficient conditions on the existence of positive periodic solutions are obtained. (English) |
| Keyword:
|
Rayleigh equations |
| Keyword:
|
positive periodic solution |
| Keyword:
|
a priori estimate |
| MSC:
|
34K13 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1224.34235 |
| idMR:
|
MR2657833 |
| DOI:
|
10.1007/s10492-010-0007-7 |
| . |
| Date available:
|
2010-07-20T13:40:20Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140393 |
| . |
| Reference:
|
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| Reference:
|
[2] Gaines, R. E., Mawhin, J. L.: Coincidence Degree and Nonlinear Differential Equations. Lecture Notes in Mathematics, No. 568.Springer Berlin-Heidelberg-New York (1977). MR 0637067 |
| Reference:
|
[3] Jiang, D., Chu, J., Zhang, M.: Multiplicity of positive periodic solutions to superlinear repulsive singular equations.J. Differ. Equations 211 (2005), 282-302. Zbl 1074.34048, MR 2125544, 10.1016/j.jde.2004.10.031 |
| Reference:
|
[4] Li, F., Liang, Z.: Existence of positive periodic solutions to nonlinear second order differential equations.Appl. Math. Lett. 18 (2005), 1256-1264. Zbl 1088.34038, MR 2170881, 10.1016/j.aml.2005.02.014 |
| Reference:
|
[5] Lin, X., Li, X., Jiang, D.: Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces.Comput. Math. Appl. 51 (2006), 507-514. MR 2207437, 10.1016/j.camwa.2005.08.030 |
| Reference:
|
[6] Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems.Springer New York (1989). Zbl 0676.58017, MR 0982267 |
| Reference:
|
[7] Yang, X.: Multiple positive solutions of second-order differential equations.Nonlinear Anal., Theory Methods Appl. 62 (2005), 107-116. Zbl 1077.34025, MR 2139358, 10.1016/j.na.2005.03.013 |
| Reference:
|
[8] Zhang, Z., Wang, J.: On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations.J. Math. Anal. Appl. 281 (2003), 99-107. Zbl 1030.34024, MR 1980077, 10.1016/S0022-247X(02)00538-3 |
| . |
