We consider a nonlinear system in the direct product of a torus and a Euclidean space. For this system, under the conditions of indefinite coercivity and indefinite monotonicity, we establish the existence of a Lipschitz invariant section.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 363–383, March, 2012.
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Samoilenko, A.M., Parasyuk, I.O. & Lahoda, V.A. Lipschitz invariant tori of indefinite-monotone systems. Ukr Math J 64, 408–432 (2012). https://doi.org/10.1007/s11253-012-0655-8
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DOI: https://doi.org/10.1007/s11253-012-0655-8