## Periodic solutions for a class of non-autonomous second order systems.(English)Zbl 1243.34057

Using the theory of critical points, the authors obtain an existence result for nontrivial periodic solution to the second-order system $\begin{cases} \ddot{u}(t)+ A \dot{u}(t)+\nabla F(t, \,u(t))=0\quad \text{a.e. }t\in [0,\,T],\\ u(0)-u(T)=0,\quad \dot{u}(0)-\dot{u}(T)=0, \end{cases}$ where $$A$$ is an antisymmetry constant matric and $$F: [0,\,T]\times\mathbb{R}^N\to\mathbb{R}$$ satisfies certain conditions. The result generalizes the work of [Z.-L. Tao, S. Yan and S.-L. Wu, “Periodic solutions for a class of superquadratic Hamiltonian systems”, J. Math. Anal. Appl. 331, No. 1, 152–158 (2007; Zbl 1123.34311)].

### MSC:

 34C25 Periodic solutions to ordinary differential equations 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 58E50 Applications of variational problems in infinite-dimensional spaces to the sciences

### Keywords:

periodic solutions; superquadratic; condition (C)$$^*$$

Zbl 1123.34311