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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

Citations:

Zbl 1123.34311
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