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Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials. (English) Zbl 1162.34328
Summary: We study the existence of infinitely many homoclinic orbits for some second-order Hamiltonian systems: $\ddot u - L(t)u(t)+\nabla F(t,u(t)) = 0, \forall t \in \bbfR$, by the variant fountain theorem, where $F(t,u)$ satisfies the super-quadratic condition $F(t,u)/|u|^{2}\rightarrow \infty $ as $|u|\rightarrow \infty $ uniformly in $t$, and need not satisfy the global Ambrosetti-Rabinowitz condition.

MSC:
34C37Homoclinic and heteroclinic solutions of ODE
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References:
[1] Mawhin, J.; Williem, M.: Critical point theory and Hamiltonian systems. 3 (1989)
[2] Ou, Z. Q.; Tang, C. L.: Existence of homoclinic solutions for the second order Hamiltonian systems. J. math. Anal. appl. 291, 203-213 (2004) · Zbl 1057.34038
[3] Zou, W. M.: Infinitely many homoclinic orbits for the second-order Hamiltonian systems. Appl. math. Lett. 16, 1283-1287 (2003) · Zbl 1039.37044
[4] Zou, W. M.: Variant Fountain theorems and their applications. Manuscripta math 104, 343-358 (2001) · Zbl 0976.35026
[5] Ding, Y. H.: Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear analysis 25, 1095-1113 (1995) · Zbl 0840.34044
[6] Xu, X. J.: Homoclinic orbits for first order Hamiltonian systems possesing super-quadratic potential. Nonlinear analysis 51, 197-214 (2002) · Zbl 1033.37031
[7] Rabinowit, P. H.: Minimax methods in critical point theory with applications to differential equations. (1986)
[8] Wu, S. P.; Liu, J. Q.: Homoclinic orbits for second order Hamiltonian system with quadratic growth. Appl. math. J. chinese univ. Ser. B. 10, 399-410 (1995) · Zbl 0841.34051
[9] Wu, S. P.; Yang, H. T.: A note on homoclinic orbits for second order Hamiltonian system. Appl. math. J. chinese univ. Ser. B 13, 251-262 (1998) · Zbl 0919.34045
[10] Fei, G.: On peoriodic solutions of superquadratic Hamiltonian systems. J. differential equations 8, 12p (2002) · Zbl 0999.37039