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High multiplicity and complexity of the bifurcation diagrams of large solutions for a class of superlinear indefinite problems
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 |
References:
[1] |
E. A. B. Ailva, Subharmonic solutions for subquadratic Hamiltonian systems, J. Diff. Eqs., 115 (1995), 120-145.
doi: 10.1006/jdeq.1995.1007. |
[2] |
K. C. Chang, "Infinite Dimensional Morse Theory and Multiple Solution Problems," Birkhäuser Boston, Inc., Boston, MA, 1993.
doi: 10.1007/978-1-4612-0385-8. |
[3] |
Y. Ding, "Variational Methods for Strongly Indefinite Problems," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. |
[4] |
I. Ekeland and H. Hofer, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Invent. Math., 81 (1985), 155-188.
doi: 10.1007/BF01388776. |
[5] |
I. Ekeland, "Convexity Method in Hamiltonian Mechanics," Springer-Verlag, Berlin, 1990.
doi: 10.1007/978-3-642-74331-3. |
[6] |
G. Fei and Q. Qiu, Minimal period solutions of nonlinear Hamiltonian systems, Nonlinear Anal., 27 (1996), 821-839.
doi: 10.1016/0362-546X(95)00077-9. |
[7] |
G. Fei, S. K. Kim and T. Wang, Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems, J. Math. Anal. Appl., 238 (1999), 216-233.
doi: 10.1006/jmaa.1999.6527. |
[8] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems, Electronic Journal of Differential Equations, 2002 (2002), 1-12. |
[9] |
Q. Jiang and S. Ma, Periodic solution for a class of subquadratic second order Hamiltonian system, Jounal of Southwest China normal University (Natural Science), 32 (2007), 6-10. |
[10] |
Sophia Th. Kyritsi and Nikolaos S. Papageorgiou, On superquadratic periodic systems with indefinite linear part, Nonlinear Anal. TMA., 72 (2010), 946-954.
doi: 10.1016/j.na.2009.07.035. |
[11] |
S. Luan and A. Mao, Periodic solutions for a class of non-autonomous Hamiltonian systems, Nonlinear Anal., 61 (2005), 1413-1426.
doi: 10.1016/j.na.2005.01.108. |
[12] |
S. Luan and A. Mao, Periodic solutions of nonautonomous second order Hamiltonian systems, Acta Mathematica Sinica, English version, 21 (2005), 685-690.
doi: 10.1007/s10114-005-0532-6. |
[13] |
S. Li and M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl., 189 (1995), 6-32.
doi: 10.1006/jmaa.1995.1002. |
[14] |
J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[15] |
K. Perera, Critical groups of critical points produced by local linking with applications, Abstr. Appl. Anal., 3 (1998), 437-446.
doi: 10.1155/S1085337598000657. |
[16] |
P. H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations," in: CBMS Regional Conf. Ser. in Math., 65, American Mathematical Society, Providence, RI, 1986. |
[17] |
P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157-184.
doi: 10.1002/cpa.3160310203. |
[18] |
M. Schechter, Periodic non-autonomous second-order dynamical systems, J. Differential Equations, 223 (2006), 290-302.
doi: 10.1016/j.jde.2005.02.022. |
[19] |
M. Schechter, "Minimax Systems and Critical Point Theory," Birkhäuser Boston, Inc., Boston, MA, 2009.
doi: 10.1007/978-0-8176-4902-9. |
[20] |
C. L. Tang, Periodic solutions of nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), 3263-3270.
doi: 10.1090/S0002-9939-98-04706-6. |
[21] |
Z. L. Tao and C. L. Tang, Periodic and subharmonic solutions of second order Hamiltonian systems, J. Math. Anal. Appl., 293 (2004), 435-445.
doi: 10.1016/j.jmaa.2003.11.007. |
[22] |
Z. L. Tao and C. L. Tang, Periodic solutions of nonquadratic second order Hamiltonian systems, (Chinese), Jounal of Southwest China normal University (Natural Science), 27 (2002), 841-846. |
[23] |
Z. L. Tao, S. Yan and S. L. Wu, Periodic solutions for a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl., 331 (2007), 152-158.
doi: 10.1016/j.jmaa.2006.08.041. |
[24] |
Y. W. Ye and C. L. Tang, Periodic and subharmonic soltions for a class of superquadratic second order Hamiltonian systems, Nonlinear Anal., 71 (2009), 2298-2307.
doi: 10.1016/j.na.2009.01.064. |
show all references
References:
[1] |
E. A. B. Ailva, Subharmonic solutions for subquadratic Hamiltonian systems, J. Diff. Eqs., 115 (1995), 120-145.
doi: 10.1006/jdeq.1995.1007. |
[2] |
K. C. Chang, "Infinite Dimensional Morse Theory and Multiple Solution Problems," Birkhäuser Boston, Inc., Boston, MA, 1993.
doi: 10.1007/978-1-4612-0385-8. |
[3] |
Y. Ding, "Variational Methods for Strongly Indefinite Problems," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. |
[4] |
I. Ekeland and H. Hofer, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Invent. Math., 81 (1985), 155-188.
doi: 10.1007/BF01388776. |
[5] |
I. Ekeland, "Convexity Method in Hamiltonian Mechanics," Springer-Verlag, Berlin, 1990.
doi: 10.1007/978-3-642-74331-3. |
[6] |
G. Fei and Q. Qiu, Minimal period solutions of nonlinear Hamiltonian systems, Nonlinear Anal., 27 (1996), 821-839.
doi: 10.1016/0362-546X(95)00077-9. |
[7] |
G. Fei, S. K. Kim and T. Wang, Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems, J. Math. Anal. Appl., 238 (1999), 216-233.
doi: 10.1006/jmaa.1999.6527. |
[8] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems, Electronic Journal of Differential Equations, 2002 (2002), 1-12. |
[9] |
Q. Jiang and S. Ma, Periodic solution for a class of subquadratic second order Hamiltonian system, Jounal of Southwest China normal University (Natural Science), 32 (2007), 6-10. |
[10] |
Sophia Th. Kyritsi and Nikolaos S. Papageorgiou, On superquadratic periodic systems with indefinite linear part, Nonlinear Anal. TMA., 72 (2010), 946-954.
doi: 10.1016/j.na.2009.07.035. |
[11] |
S. Luan and A. Mao, Periodic solutions for a class of non-autonomous Hamiltonian systems, Nonlinear Anal., 61 (2005), 1413-1426.
doi: 10.1016/j.na.2005.01.108. |
[12] |
S. Luan and A. Mao, Periodic solutions of nonautonomous second order Hamiltonian systems, Acta Mathematica Sinica, English version, 21 (2005), 685-690.
doi: 10.1007/s10114-005-0532-6. |
[13] |
S. Li and M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl., 189 (1995), 6-32.
doi: 10.1006/jmaa.1995.1002. |
[14] |
J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[15] |
K. Perera, Critical groups of critical points produced by local linking with applications, Abstr. Appl. Anal., 3 (1998), 437-446.
doi: 10.1155/S1085337598000657. |
[16] |
P. H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations," in: CBMS Regional Conf. Ser. in Math., 65, American Mathematical Society, Providence, RI, 1986. |
[17] |
P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157-184.
doi: 10.1002/cpa.3160310203. |
[18] |
M. Schechter, Periodic non-autonomous second-order dynamical systems, J. Differential Equations, 223 (2006), 290-302.
doi: 10.1016/j.jde.2005.02.022. |
[19] |
M. Schechter, "Minimax Systems and Critical Point Theory," Birkhäuser Boston, Inc., Boston, MA, 2009.
doi: 10.1007/978-0-8176-4902-9. |
[20] |
C. L. Tang, Periodic solutions of nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), 3263-3270.
doi: 10.1090/S0002-9939-98-04706-6. |
[21] |
Z. L. Tao and C. L. Tang, Periodic and subharmonic solutions of second order Hamiltonian systems, J. Math. Anal. Appl., 293 (2004), 435-445.
doi: 10.1016/j.jmaa.2003.11.007. |
[22] |
Z. L. Tao and C. L. Tang, Periodic solutions of nonquadratic second order Hamiltonian systems, (Chinese), Jounal of Southwest China normal University (Natural Science), 27 (2002), 841-846. |
[23] |
Z. L. Tao, S. Yan and S. L. Wu, Periodic solutions for a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl., 331 (2007), 152-158.
doi: 10.1016/j.jmaa.2006.08.041. |
[24] |
Y. W. Ye and C. L. Tang, Periodic and subharmonic soltions for a class of superquadratic second order Hamiltonian systems, Nonlinear Anal., 71 (2009), 2298-2307.
doi: 10.1016/j.na.2009.01.064. |
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