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March  2011, 31(1): 25-34. doi: 10.3934/dcds.2011.31.25

Estimates on the number of limit cycles of a generalized Abel equation

1. 

Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain, Spain

Received  May 2010 Revised  March 2011 Published  June 2011

We prove new results about the number of isolated periodic solutions of a first order differential equation with a polynomial nonlinearity. Such results are applied to bound the number of limit cycles of a family of planar polynomial vector fields which generalize the so-called rigid systems.
Citation: Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25
References:
[1]

Communications on Pure and Applied Analysis, 8 (2009), 1493-1501. doi: 10.3934/cpaa.2009.8.1493.  Google Scholar

[2]

J. Math. Anal. Appl., 329 (2007), 1161-1169. doi: 10.1016/j.jmaa.2006.07.039.  Google Scholar

[3]

Discrete and Continuos Dynamical Systems, 25 (2009), 1129-1141. doi: 10.3934/dcds.2009.25.1129.  Google Scholar

[4]

M. A. M. Alwash, Periodic solutions of polynomial non-autonomous differential equations,, Electronic Journal of Differential Equations, 2005 (): 1.   Google Scholar

[5]

Advances in Differential Equations, 7 (2002), 197-216.  Google Scholar

[6]

Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), 3737-3745. doi: 10.1142/S0218127406017130.  Google Scholar

[7]

Proc. Amer. Math. Soc., 133 (2005), 751-758. doi: 10.1090/S0002-9939-04-07542-2.  Google Scholar

[8]

Nonlinear Analysis, 71 (2009), 1941-1949. doi: 10.1016/j.na.2009.01.034.  Google Scholar

[9]

Nonlinearity, 13 (2000), 1337-1342. doi: 10.1088/0951-7715/13/4/319.  Google Scholar

[10]

J. Math. Anal. Appl., 194 (1995), 763-779. doi: 10.1006/jmaa.1995.1328.  Google Scholar

[11]

Mathematics in Science and Engineering, 30, Academic Press, New York, 1966. Google Scholar

[12]

Inv. Math., 59 (1980), 67-76. doi: 10.1007/BF01390315.  Google Scholar

[13]

J. Math. Anal. Appl., 140 (1989), 381-395. doi: 10.1016/0022-247X(89)90072-3.  Google Scholar

[14]

J. London Math. Soc., 20 (1979), 277-286. doi: 10.1112/jlms/s2-20.2.277.  Google Scholar

[15]

Math. Notes, 64 (1998), 622-628. doi: 10.1007/BF02316287.  Google Scholar

[16]

Academic Press, New York, 1966. Google Scholar

[17]

J. Math. Anal. Appl., 159 (1991), 127-146. doi: 10.1016/0022-247X(91)90225-O.  Google Scholar

show all references

References:
[1]

Communications on Pure and Applied Analysis, 8 (2009), 1493-1501. doi: 10.3934/cpaa.2009.8.1493.  Google Scholar

[2]

J. Math. Anal. Appl., 329 (2007), 1161-1169. doi: 10.1016/j.jmaa.2006.07.039.  Google Scholar

[3]

Discrete and Continuos Dynamical Systems, 25 (2009), 1129-1141. doi: 10.3934/dcds.2009.25.1129.  Google Scholar

[4]

M. A. M. Alwash, Periodic solutions of polynomial non-autonomous differential equations,, Electronic Journal of Differential Equations, 2005 (): 1.   Google Scholar

[5]

Advances in Differential Equations, 7 (2002), 197-216.  Google Scholar

[6]

Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), 3737-3745. doi: 10.1142/S0218127406017130.  Google Scholar

[7]

Proc. Amer. Math. Soc., 133 (2005), 751-758. doi: 10.1090/S0002-9939-04-07542-2.  Google Scholar

[8]

Nonlinear Analysis, 71 (2009), 1941-1949. doi: 10.1016/j.na.2009.01.034.  Google Scholar

[9]

Nonlinearity, 13 (2000), 1337-1342. doi: 10.1088/0951-7715/13/4/319.  Google Scholar

[10]

J. Math. Anal. Appl., 194 (1995), 763-779. doi: 10.1006/jmaa.1995.1328.  Google Scholar

[11]

Mathematics in Science and Engineering, 30, Academic Press, New York, 1966. Google Scholar

[12]

Inv. Math., 59 (1980), 67-76. doi: 10.1007/BF01390315.  Google Scholar

[13]

J. Math. Anal. Appl., 140 (1989), 381-395. doi: 10.1016/0022-247X(89)90072-3.  Google Scholar

[14]

J. London Math. Soc., 20 (1979), 277-286. doi: 10.1112/jlms/s2-20.2.277.  Google Scholar

[15]

Math. Notes, 64 (1998), 622-628. doi: 10.1007/BF02316287.  Google Scholar

[16]

Academic Press, New York, 1966. Google Scholar

[17]

J. Math. Anal. Appl., 159 (1991), 127-146. doi: 10.1016/0022-247X(91)90225-O.  Google Scholar

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