具有凸位势的Poisson梯度动力系统
Poisson-Gradient Dynamical Systems with Convex Potential
摘要：
主要目的是将具有凸位势的非自治二阶微分系统的一些结果和概念推广到具有凸位势的多时间Poisson梯度PDE系统.在这个意义上，我们证明了一个合适的作用泛函的极小是多个周期解的狄利克雷问题相关的Euler-Lagrange方程。自动地，这些是相关联的多时间哈密顿方程的解。
英文摘要：
The basic aim is to extend some results and concepts of non-autonomous second order differential systems with convex potentials to the new context of multi-time Poisson-gradient PDE systems with convex potential. In this sense, we prove that minimizers of a suitable action functional are multiple periodical solutions of a Dirichlet problem associated to the Euler-Lagrange equations. Automatically, these are solutions of the associated multi-time Hamiltonian equations.
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