Existence of the time periodic solutions of system of oscillators on $2D$-lattice

S.M. Bak

Existence of the time periodic solutions of system of oscillators on $2D$ -lattice

Authors

S.M. Bak Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, Vinnytsia, Ukraine

Keywords:

oscillator system, periodic solutions, mountain pass theorem

Published online: 2012-12-27

Abstract

It is considered the system of differential equations that describes the dynamics of an infinite system of oscillators on $2D$ -lattice. Results on existence of the time periodic solutions are obtained. By means of the mountain pass theorem, it is obtained sufficient conditions for the existence of such solutions.