Affiliation:
1. Mykhailo Kotsyubynskyi Vinnytsia State Pedagogical University, Vinnytsia, Ukraine
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.
Publisher
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
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