Global well-posedness of the Cauchy problem for a system of oscillators on a 2D-lattice with power potentials

摘要

Abstract We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two-dimensional integer-valued lattice. We prove a result on the existence and uniqueness of global solutions of the Cauchy problem for such systems with power potentials. Moreover, a result on the nonexistence of global solutions is obtained.