On the number of limit cycles of a generalized Abel equation

Naeem Alkoumi; Pedro J. Torres

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 73-83
  • ISSN: 0011-4642

Abstract

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New results are proved on the maximum number of isolated T -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.

How to cite

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Alkoumi, Naeem, and Torres, Pedro J.. "On the number of limit cycles of a generalized Abel equation." Czechoslovak Mathematical Journal 61.1 (2011): 73-83. <http://eudml.org/doc/197103>.

@article{Alkoumi2011,
abstract = {New results are proved on the maximum number of isolated $T$-periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.},
author = {Alkoumi, Naeem, Torres, Pedro J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {periodic solution; limit cycle; polynomial nonlinearity; periodic solution; limit cycle; polynomial nonlinearity},
language = {eng},
number = {1},
pages = {73-83},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the number of limit cycles of a generalized Abel equation},
url = {http://eudml.org/doc/197103},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Alkoumi, Naeem
AU - Torres, Pedro J.
TI - On the number of limit cycles of a generalized Abel equation
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 73
EP - 83
AB - New results are proved on the maximum number of isolated $T$-periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.
LA - eng
KW - periodic solution; limit cycle; polynomial nonlinearity; periodic solution; limit cycle; polynomial nonlinearity
UR - http://eudml.org/doc/197103
ER -

References

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  2. Álvarez, M. J., Gasull, A., Giacomini, H., 10.1016/j.jde.2006.11.004, J. Differ. Equations 234 (2007), 161-176. (2007) MR2298969DOI10.1016/j.jde.2006.11.004
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  9. Gasull, A., Torregrosa, J., 10.1090/S0002-9939-04-07542-2, Proc. Am. Math. Soc. 133 (2005), 751-758. (2005) Zbl1062.34030MR2113924DOI10.1090/S0002-9939-04-07542-2
  10. Korman, P., Ouyang, T., 10.1006/jmaa.1995.1328, J. Math. Anal. Appl. 194 (1995), 763-379. (1995) Zbl0844.34036MR1350195DOI10.1006/jmaa.1995.1328
  11. Lins-Neto, A., On the number of solutions of the equation ∑ j = 0 n a j ( t ) x j , 0 ≤ t ≤ 1 , for which x ( 0 ) = x ( 1 ) , Invent. Math. 59 (1980), 69-76. (1980) 
  12. Nkashama, M. N., 10.1016/0022-247X(89)90072-3, J. Math. Anal. Appl. 140 (1989), 381-395. (1989) Zbl0674.34009MR1001864DOI10.1016/0022-247X(89)90072-3
  13. Pliss, V. A., Nonlocal Problems of the Theory of Oscillations, Academic Press New York (1966). (1966) Zbl0151.12104MR0196199
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