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Periodic solutions for second order Hamiltonian systems with a change sign potential. (English) Zbl 1078.34023
The authors deal with the following second-order Hamiltonian system $$\gathered u''(t)+ b(t)\nabla V(u(t))= 0\quad\text{a.e. }t\i [0,T],\\ u(0)- u(T)= \dot u(0)- \dot u(T)= 0,\endgathered\tag1$$ with $T> 0$, $b\in C([0,T],\bbfR)$ and $V\in C^1(\bbfR^N, \bbfR)$. In contrast to many papers, the authors assume that $b$ changes sign and $\int^T_0 b(t)\,dt= 0$. Using the minimax methods in critical point theory, the authors prove the existence of at least one nonzero solution of (1) under suitable assumptions on $V$.

34C25Periodic solutions of ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
Full Text: DOI
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