Existence of Lipschitz Tori for Nonlinear Systems with Lag

Assume that the right-hand side of (2.1) satisfies the following conditions in the region 

Under these assumptions, we now find the conditions which ensure the existence of an invariant toroidal manifold tt y = H((p) of the system (2.1) whose derivatives satisfy the Lipschitz conditions. To find this torus, we use, as before, an iteration process. 

Existence ofLipschitz Tori for Nonlinear Systems with Lag 

7) holds, then there exists a Green s function of the problem concerning the invariant tori of the system (2.4) which has the form (Samoilenko, 1970a) 

Let US now find conditions under which the system (2.4) possesses an invariant torus. Since f2 ((p, i) = E, the estimate (2.7) implies that the inequalities 

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