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Method of positively invariant cones for evolution systems with cubic and periodic nonlinearities

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Abstract

We consider the method of positively invariant cones for evolution equations with a cubic nonlinearity of the Duffing type and with a periodic nonlinearity. For equations of the first type, we prove the existence of a positively invariant bounded set. For equations of the second type, we show that the solutions are bounded. We present a lemma on the nonstrict separation of quadratic cones in a rigged Hilbert space.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    S. A. Popov

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  1. S. A. Popov
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Correspondence to S. A. Popov.

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Popov, S.A. Method of positively invariant cones for evolution systems with cubic and periodic nonlinearities. Diff Equat 50, 1739–1751 (2014). https://doi.org/10.1134/S0012266114130059

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  • DOI: https://doi.org/10.1134/S0012266114130059

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