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Subharmonic solutions for a class of non-quadratic second order Hamiltonian systems. (English) Zbl 1254.37042
The authors prove the infinity of subharmonic solutions of second order Hamiltonian systems under non-quadratic conditions by using the mini-max principle. The results extend and improve some known results.
MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
58E50Applications of variational methods in infinite-dimensional spaces
34C25Periodic solutions of ODE
References:
[1]Mawhin, J.; Willem, M.: Critical point theory and Hamiltonian systems, (1989)
[2]Tang, C. L.: Periodic solutions of nonautonomous second order systems with sublinear nonlinearity, Proc. amer. Math. soc. 126, 3263-3270 (1998) · Zbl 0902.34036 · doi:10.1090/S0002-9939-98-04706-6
[3]Ailva, E. A. B.: Subharmonic solutions for subquadratic Hamiltonian systems, J. differential equations 115, 120-145 (1995) · Zbl 0814.34025 · doi:10.1006/jdeq.1995.1007
[4]Schechter, M.: Periodic non-autonomous second-order dynamical systems, J. differential equations 223, No. 2, 290-302 (2006) · Zbl 1099.34042 · doi:10.1016/j.jde.2005.02.022
[5]Rabinowitz, P. H.: Minimax methods in critical point theory with applications to differential equations, CBMS regional conf. Ser. in math. 65 (1986) · Zbl 0609.58002
[6]Rabinowitz, P. H.: Periodic solutions of Hamiltonian systems, Comm. pure appl. Math. 31, 157-184 (1978) · Zbl 0358.70014 · doi:10.1002/cpa.3160310203
[7]Chang, K. C.: Infinite dimensional Morse theory and multiple solution problems, Progress in nonlinear differential equations and their applications 6 (1993) · Zbl 0779.58005
[8]Ekeland, I.: Convexity method in Hamiltonian mechanics, (1990)
[9]Ekeland, I.; Hofer, H.: Periodic solutions with prescribed period for convex autonomous Hamiltonian systems, Invent. math. 81, 155-188 (1985) · Zbl 0594.58035 · doi:10.1007/BF01388776
[10]Fei, G.; Qiu, Q.: Minimal periodic solutions of nonlinear Hamiltonian systems, Nonlinear anal. 27, 821-839 (1996) · Zbl 0858.34034 · doi:10.1016/0362-546X(95)00077-9
[11]Fei, G.; Kim, S.; Wang, T.: Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems, J. math. Anal. appl. 238, 216-233 (1999) · Zbl 0936.34032 · doi:10.1006/jmaa.1999.6527
[12]Fei, G.: On periodic solutions of superquadratic Hamiltonian systems, Electron. J. Differential equations 2002, No. 8, 1-12 (2002) · Zbl 0999.37039 · doi:emis:journals/EJDE/Volumes/2002/08/abstr.html
[13]Tao, Z. L.; Tang, C. L.: Periodic and subharmonic soltions of second order Hamiltonian systems, J. math. Anal. appl. 293, 435-445 (2004) · Zbl 1042.37047 · doi:10.1016/j.jmaa.2003.11.007
[14]Ye, Y. W.; Tang, C. L.: Periodic solutions for some nonautonomous second order Hamiltonian systems, J. math. Anal. appl. 344, No. 1, 462-471 (2008) · Zbl 1142.37023 · doi:10.1016/j.jmaa.2008.03.021
[15]Benci, V.; Rabinowitz, P. H.: Critical point theorems for indefinite functions, Invent. math. 52, 241-273 (1979) · Zbl 0465.49006 · doi:10.1007/BF01389883
[16]Ding, Y.: Variational methods for strongly indefinite problems, Interdisciplinary mathematical sciences 7 (2007)
[17]Bartolo, P.; Benci, V.; Fortunato, D.: Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear anal. 7, 241-273 (1983) · Zbl 0522.58012 · doi:10.1016/0362-546X(83)90115-3
[18]Krosnoselski, M. A.: Topological methods in the theory of nonlinear integral equations, (1964) · Zbl 0111.30303