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Infinitely many periodic solutions for a second-order nonautonomous system. (English) Zbl 1055.34082

The existence of solutions \(u\in C^1([0,T],\mathbb{R}^k)\) to the system \[ \ddot u= A(t)u+ b(t)\nabla G(u)\quad\text{a.e. in }[0,T],\quad u(0)- u(T)= \dot u(0)-\dot u(T)= 0,\tag{1} \] is investigated. Roughly speaking, it is shown that if \(G\) has a suitable oscillation behavior at infinity (or at zero), then (1) has an unbounded sequence of solutions (or a sequence of nonzero solutions tending to zero). The proofs are based on a recent local minima result by R. Ricceri.

MSC:

34C25 Periodic solutions to ordinary differential equations
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