April  2013, 33(4): 1603-1614. doi: 10.3934/dcds.2013.33.1603

Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations

1. 

Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Av. Esteve Terradas 5, 08860 Castelldefels, Spain

2. 

Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Received  October 2011 Revised  May 2012 Published  October 2012

This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-auto-nomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.
Citation: Josep M. Olm, Xavier Ros-Oton. Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1603-1614. doi: 10.3934/dcds.2013.33.1603
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show all references

References:
[1]

J. Math. Anal. Applic., 328 (2007), 1108-1116. doi: 10.1016/j.jmaa.2006.05.078.  Google Scholar

[2]

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

[3]

$2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton, 2003.  Google Scholar

[4]

Math. Intelligencer, 20 (1998), 7-15. doi: 10.1007/BF03025291.  Google Scholar

[5]

SIAM J. Math. Anal., 21 (1990), 1235-1244. doi: 10.1137/0521068.  Google Scholar

[6]

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

[7]

J. Differential Equations, 234 (2007), 161-176. doi: 10.1016/j.jde.2006.11.004.  Google Scholar

[8]

J. Math. Anal. Applic, 342 (2008), 931-942. doi: 10.1016/j.jmaa.2007.12.060.  Google Scholar

[9]

Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19 (2009), 3869-3876. doi: 10.1142/S0218127409025195.  Google Scholar

[10]

Discrete Continuous Dynam. Systems - A, 25 (2009), 1129-1141. doi: 10.3934/dcds.2009.25.1129.  Google Scholar

[11]

Discrete Continuous Dynam. Systems - A, 31 (2011), 25-34. doi: 10.3934/dcds.2011.31.25.  Google Scholar

[12]

J. Math. Anal. Appl., 381 (2011), 582-589. doi: 10.1016/j.jmaa.2011.02.084.  Google Scholar

[13]

Discrete Continuous Dynam. Systems - B, 7 (2007), 53-76.  Google Scholar

[14]

Discrete Continuous Dynam. Systems - B, 15 (2011), 197-215. doi: 10.3934/dcdsb.2011.15.197.  Google Scholar

[15]

J. Differential Equations, 185 (2002), 54-73. doi: 10.1006/jdeq.2002.4172.  Google Scholar

[16]

J. Differential Equations, 3 (1967), 546-570.  Google Scholar

[17]

$2^{nd}$ edition, Springer-Verlag, New York, 1985.  Google Scholar

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