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

Method of positively invariant cones for evolution systems with cubic and periodic nonlinearities 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

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

Differential Equations , Volume 50 (13) – Jan 31, 2015

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266114130059
Publisher site
See Article on Publisher Site

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.

Journal

Differential EquationsSpringer Journals

Published: Jan 31, 2015

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