New results on periodic solutions for a kind of Rayleigh equation

Mei-Lan Tang; Xin-Ge Liu; Xin-Bi Liu

Applications of Mathematics (2009)

  • Volume: 54, Issue: 1, page 79-85
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Tang, Mei-Lan, Liu, Xin-Ge, and Liu, Xin-Bi. "New results on periodic solutions for a kind of Rayleigh equation." Applications of Mathematics 54.1 (2009): 79-85. <http://eudml.org/doc/37809>.

@article{Tang2009,
abstract = {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.},
author = {Tang, Mei-Lan, Liu, Xin-Ge, Liu, Xin-Bi},
journal = {Applications of Mathematics},
keywords = {Rayleigh equations; existence; periodic solution; a priori estimate; existence; periodic solution; a priori estimate},
language = {eng},
number = {1},
pages = {79-85},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New results on periodic solutions for a kind of Rayleigh equation},
url = {http://eudml.org/doc/37809},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Tang, Mei-Lan
AU - Liu, Xin-Ge
AU - Liu, Xin-Bi
TI - New results on periodic solutions for a kind of Rayleigh equation
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 79
EP - 85
AB - 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.
LA - eng
KW - Rayleigh equations; existence; periodic solution; a priori estimate; existence; periodic solution; a priori estimate
UR - http://eudml.org/doc/37809
ER -

References

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  1. Chen, F. D., Existence and uniqueness of almost periodic solutions for forced Rayleigh equations, Ann. Differ. Equations 17 (2001), 1-9. (2001) MR1829382
  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. (2005) MR2157759
  3. Deimling, K., Nonlinear Functional Analysis, Springer Berlin (1985). (1985) Zbl0559.47040
  4. Gaines, R. E., Mawhin, J. L., Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics, Vol. 568, Springer Berlin (1977). (1977) 
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  6. Liu, F., On the existence of the periodic solutions of Rayleigh equation, Acta Math. Sin. 37 (1994), 639-644 Chinese. (1994) Zbl0812.34037
  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. (2004) Zbl1078.34048MR2035324
  8. Lu, S. P., Ge, W. G., Zheng, Z. X., 10.1016/S0893-9659(04)90087-0, Appl. Math. Lett. 17 (2004), 443-449. (2004) Zbl1073.34081MR2045750DOI10.1016/S0893-9659(04)90087-0
  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. (2004) Zbl1073.34081MR2074353
  10. Peng, L., 10.1016/j.jfranklin.2006.04.001, J. Franklin Inst. 7 (2006), 676-687. (2006) Zbl1114.34051MR2293410DOI10.1016/j.jfranklin.2006.04.001
  11. Wang, G.-Q., Cheng, S. S., 10.1016/S0893-9659(98)00169-4, Appl. Math. Lett. 12 (1999), 41-44. (1999) Zbl0980.34068DOI10.1016/S0893-9659(98)00169-4
  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. (2000) Zbl0963.34069
  13. Wang, G.-Q., Yan, J. R., 10.1155/S0161171200001836, Int. J. Math. Math. Sci. 23 (2000), 65-68. (2000) Zbl0949.34059DOI10.1155/S0161171200001836
  14. Zhou, Y., Tang, X., 10.1016/j.cam.2006.03.002, J. Comput. Appl. Math. 203 (2007), 1-5. (2007) Zbl1115.34067MR2313817DOI10.1016/j.cam.2006.03.002

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