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Infinitely many periodic solutions for subquadratic second-order Hamiltonian systems. (English) Zbl 1294.34047

Summary: Consider the second-order Hamiltonian systems \[ \begin{aligned} & \ddot u(t)+\nabla_uW(t,u)=0\quad\forall t\in\mathbb R,\\ & u(0)=u(T),\quad \dot u(0)=\dot u(T),\quad T>0,\end{aligned} \] where \(W(t,u)\) is \(T\)-periodic in \(t\). We investigate the existence of infinitely many periodic solutions for a class of subquadratic nonautonomous second-order Hamiltonian systems by using the variant fountain theorem.

MSC:

34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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[1] Chen G, Ma S: Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum 0. J. Math. Anal. Appl. 2011, 379: 842-851. 10.1016/j.jmaa.2011.02.013
[2] Ding Y, Lee C: Periodic solutions for Hamiltonian systems. SIAM J. Math. Anal. 2000, 32: 555-571. 10.1137/S0036141099358178
[3] He X, Wu X: Periodic solutions for a class of nonautonomous second order Hamiltonian systems. J. Math. Anal. Appl. 2008, 341(2):1354-1364. 10.1016/j.jmaa.2007.11.028
[4] Jiang Q, Tang C: Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems. J. Math. Anal. Appl. 2007, 328: 380-389. 10.1016/j.jmaa.2006.05.064
[5] Wang Z, Zhang J: Periodic solutions of a class of second order non-autonomous Hamiltonian systems. Nonlinear Anal. 2010, 72: 4480-4487. 10.1016/j.na.2010.02.023
[6] Zhang Q, Liu C: Infinitely many periodic solutions for second-order Hamiltonian systems. J. Differ. Equ. 2011, 251: 816-833. 10.1016/j.jde.2011.05.021
[7] Zou W: Multiple solutions for second-order Hamiltonian systems via computation of the critical groups. Nonlinear Anal. TMA 2001, 44: 975-989. 10.1016/S0362-546X(99)00324-7
[8] Zou W: Variant fountain theorems and their applications. Manuscr. Math. 2001, 104: 343-358. 10.1007/s002290170032
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