Periodic solutions for a class of Lorenz-Lagrangian systems
The author studies a class of Lorentz-Lagrange systems of the form (*) \(- A\ddot q=\nabla V(q)\) where \(q\in R^ n\), A is a real symmetric matrix with eigenvalues \(\lambda_ i\) \((\lambda_ 1<0)\) and corresponding eigenvectors \(e_ i\) \((1\leq i\leq n)\). By improving some ideas developed in previous papers [\textit{H. Hofer} and \textit{J. Toland}, Math. Ann. 268, 387-403 (1984; Zbl 0569.70017); \textit{J. Toland} [Nonlinear Functional Analysis and its Applications, Proc. NATO Adv. Study Inst. Maratea/Italy 1985, NATO ASI Ser., Ser. C 173, 147-160 (1986; Zbl 0606.58023)] and introducing a new idea, the existence of a periodic solution of the system (*) is proved under hypotheses which involve only the set where \(V>0\).
scientific article; zbMATH DE number 4073480