On the global solvability of the Cauchy problem for an infinite system of differential equations (Q981988)

Consider the lattice differential equation \[ \dot y_1= -y_1y_2,\quad \dot y_n= y_n(y_{n-1}- y_{n+1}),\quad n= 2,3,\dots\;.\tag{\(*\)} \] The author proves the unique existence of a solution to \((*)\) satisfying the initial condition \[ y_n(0)= y^0_n,\quad \sum^\infty_{n=1} n|y^0_n-\widehat y_n|< \infty, \] where \(\widehat y_n\), \(\widehat y_{n+2}=\widehat y_n\), is a given periodic sequence, and which belongs to some function space.