Periodical Solutions of Poisson-Gradient Dynamical Systems with Periodical Potential

Abstract

The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. The Section 1 establishes the basic tools. The section 2 underlines conditions in which the action $\varphi (u)={\int }_{T_0}[$, that produces the Poisson-gradient systems, is continuous, and some conditions in which the general action $\varphi (u)={\int }_{T_0}L(t,u(t),\frac{\partial u}{\partial t}(t))d{t}^1\wedge >...\wedge d{t}^p$ is continuously differentiable. The Section 3 studies the multiple periodical solutions of a Poisson-gradient system in the case when the potential function $F$ has a spatial periodicity.

14 pages, Key words: variational methods, elliptic systems, multi-periodic solutions; Communicated at 8-th International Conference of Tensor Society, August 22-26, 2005, Varna, Bulgaria