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January  2014, 13(1): 75-95. doi: 10.3934/cpaa.2014.13.75

Some united existence results of periodic solutions for non-quadratic second order Hamiltonian systems

1. 

Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, China

2. 

School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, China

Received  May 2011 Revised  April 2012 Published  July 2013

In this paper, some existence theorems are obtained for periodic solutions of second order Hamiltonian systems under non-quadratic conditions by using the minimax principle. Our results unite, extend and improve those relative works in some known literature.
Citation: Xingyong Zhang, Xianhua Tang. Some united existence results of periodic solutions for non-quadratic second order Hamiltonian systems. Communications on Pure & Applied Analysis, 2014, 13 (1) : 75-95. doi: 10.3934/cpaa.2014.13.75
References:
[1]

J. Diff. Eqs., 115 (1995), 120-145. doi: 10.1006/jdeq.1995.1007.  Google Scholar

[2]

Birkhäuser Boston, Inc., Boston, MA, 1993. doi: 10.1007/978-1-4612-0385-8.  Google Scholar

[3]

World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.  Google Scholar

[4]

Invent. Math., 81 (1985), 155-188. doi: 10.1007/BF01388776.  Google Scholar

[5]

Springer-Verlag, Berlin, 1990. doi: 10.1007/978-3-642-74331-3.  Google Scholar

[6]

Nonlinear Anal., 27 (1996), 821-839. doi: 10.1016/0362-546X(95)00077-9.  Google Scholar

[7]

J. Math. Anal. Appl., 238 (1999), 216-233. doi: 10.1006/jmaa.1999.6527.  Google Scholar

[8]

Electronic Journal of Differential Equations, 2002 (2002), 1-12.  Google Scholar

[9]

Jounal of Southwest China normal University (Natural Science), 32 (2007), 6-10. Google Scholar

[10]

Nonlinear Anal. TMA., 72 (2010), 946-954. doi: 10.1016/j.na.2009.07.035.  Google Scholar

[11]

Nonlinear Anal., 61 (2005), 1413-1426. doi: 10.1016/j.na.2005.01.108.  Google Scholar

[12]

Acta Mathematica Sinica, English version, 21 (2005), 685-690. doi: 10.1007/s10114-005-0532-6.  Google Scholar

[13]

J. Math. Anal. Appl., 189 (1995), 6-32. doi: 10.1006/jmaa.1995.1002.  Google Scholar

[14]

Springer-Verlag, New York, 1989. doi: 10.1007/978-1-4757-2061-7.  Google Scholar

[15]

Abstr. Appl. Anal., 3 (1998), 437-446. doi: 10.1155/S1085337598000657.  Google Scholar

[16]

in: CBMS Regional Conf. Ser. in Math., 65, American Mathematical Society, Providence, RI, 1986.  Google Scholar

[17]

Comm. Pure Appl. Math., 31 (1978), 157-184. doi: 10.1002/cpa.3160310203.  Google Scholar

[18]

J. Differential Equations, 223 (2006), 290-302. doi: 10.1016/j.jde.2005.02.022.  Google Scholar

[19]

Birkhäuser Boston, Inc., Boston, MA, 2009. doi: 10.1007/978-0-8176-4902-9.  Google Scholar

[20]

Proc. Amer. Math. Soc. 126 (1998), 3263-3270. doi: 10.1090/S0002-9939-98-04706-6.  Google Scholar

[21]

J. Math. Anal. Appl., 293 (2004), 435-445. doi: 10.1016/j.jmaa.2003.11.007.  Google Scholar

[22]

(Chinese), Jounal of Southwest China normal University (Natural Science), 27 (2002), 841-846. Google Scholar

[23]

J. Math. Anal. Appl., 331 (2007), 152-158. doi: 10.1016/j.jmaa.2006.08.041.  Google Scholar

[24]

Nonlinear Anal., 71 (2009), 2298-2307. doi: 10.1016/j.na.2009.01.064.  Google Scholar

show all references

References:
[1]

J. Diff. Eqs., 115 (1995), 120-145. doi: 10.1006/jdeq.1995.1007.  Google Scholar

[2]

Birkhäuser Boston, Inc., Boston, MA, 1993. doi: 10.1007/978-1-4612-0385-8.  Google Scholar

[3]

World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.  Google Scholar

[4]

Invent. Math., 81 (1985), 155-188. doi: 10.1007/BF01388776.  Google Scholar

[5]

Springer-Verlag, Berlin, 1990. doi: 10.1007/978-3-642-74331-3.  Google Scholar

[6]

Nonlinear Anal., 27 (1996), 821-839. doi: 10.1016/0362-546X(95)00077-9.  Google Scholar

[7]

J. Math. Anal. Appl., 238 (1999), 216-233. doi: 10.1006/jmaa.1999.6527.  Google Scholar

[8]

Electronic Journal of Differential Equations, 2002 (2002), 1-12.  Google Scholar

[9]

Jounal of Southwest China normal University (Natural Science), 32 (2007), 6-10. Google Scholar

[10]

Nonlinear Anal. TMA., 72 (2010), 946-954. doi: 10.1016/j.na.2009.07.035.  Google Scholar

[11]

Nonlinear Anal., 61 (2005), 1413-1426. doi: 10.1016/j.na.2005.01.108.  Google Scholar

[12]

Acta Mathematica Sinica, English version, 21 (2005), 685-690. doi: 10.1007/s10114-005-0532-6.  Google Scholar

[13]

J. Math. Anal. Appl., 189 (1995), 6-32. doi: 10.1006/jmaa.1995.1002.  Google Scholar

[14]

Springer-Verlag, New York, 1989. doi: 10.1007/978-1-4757-2061-7.  Google Scholar

[15]

Abstr. Appl. Anal., 3 (1998), 437-446. doi: 10.1155/S1085337598000657.  Google Scholar

[16]

in: CBMS Regional Conf. Ser. in Math., 65, American Mathematical Society, Providence, RI, 1986.  Google Scholar

[17]

Comm. Pure Appl. Math., 31 (1978), 157-184. doi: 10.1002/cpa.3160310203.  Google Scholar

[18]

J. Differential Equations, 223 (2006), 290-302. doi: 10.1016/j.jde.2005.02.022.  Google Scholar

[19]

Birkhäuser Boston, Inc., Boston, MA, 2009. doi: 10.1007/978-0-8176-4902-9.  Google Scholar

[20]

Proc. Amer. Math. Soc. 126 (1998), 3263-3270. doi: 10.1090/S0002-9939-98-04706-6.  Google Scholar

[21]

J. Math. Anal. Appl., 293 (2004), 435-445. doi: 10.1016/j.jmaa.2003.11.007.  Google Scholar

[22]

(Chinese), Jounal of Southwest China normal University (Natural Science), 27 (2002), 841-846. Google Scholar

[23]

J. Math. Anal. Appl., 331 (2007), 152-158. doi: 10.1016/j.jmaa.2006.08.041.  Google Scholar

[24]

Nonlinear Anal., 71 (2009), 2298-2307. doi: 10.1016/j.na.2009.01.064.  Google Scholar

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