TY - JOUR AU - Xiao, Huafeng AU - Shen, Zupei PY - 2020 DA - 2020/12/09 TI - Periodic solutions with prescribed minimal period to Hamiltonian systems JO - Journal of Inequalities and Applications SP - 257 VL - 2020 IS - 1 AB - In this article, we study the existence of periodic solutions to second order Hamiltonian systems. Our goal is twofold. When the nonlinear term satisfies a strictly monotone condition, we show that, for any $T>0$, there exists a T-periodic solution with minimal period T. When the nonlinear term satisfies a non-decreasing condition, using a perturbation technique, we prove a similar result. In the latter case, the periodic solution corresponds to a critical point which minimizes the variational functional on the Nehari manifold which is not homeomorphic to the unit sphere. SN - 1029-242X UR - https://doi.org/10.1186/s13660-020-02524-4 DO - 10.1186/s13660-020-02524-4 ID - Xiao2020 ER -