ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Method of Positively Invariant Cones for Evolutionary Systems with Cubic and Periodic Nonlinearities


Sergei Albertovich Popov

Saint-Petersburg State University


We investigate the method of positively invariant cones for evolutionary variational equations with monotone nonlinearities in a rigged Hilbert space structure. A theorem of existence and uniqueness is stated for such class of systems. In the paper we consider cubic nonlinearity of Duffing-type and periodic nonlinearity. The existense of a positively invariant bounded set is proved for equations of the first type. The boundedness of solutions is proved for equations of the second type. A lemma on non-strict seperation of quadratic cones in a rigged Hilbert space is stated.


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