Massera's theorem for quasi-periodic differential equations
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Bounded, recurrent and quasi-periodic solutions, partial differential equations on the torusAbstrakt
For a scalar, first order ordinary differential equation which depends periodically on time, Massera's Theorem says that the existence of a bounded solution implies the existence of a periodic solution. Though the statement is false when periodicity is replaced by quasi-periodicity, solutions with some kind of recurrence are anyway expected when the equation is quasi-periodic in time. Indeed we first prove that the existence of a bounded solution implies the existence of a solution which is quasi-periodic in a weak sense. The partial differential equation, having our original equation as its equation of characteristics, plays a key role in the introduction of this notion of weak quasi-periodicity. Then we compare our approach with others already known in the literature. Finally, we give an explicit example of the weak case, and an extension to higher dimension for a special class of equations.Pobrania
Opublikowane
2002-03-01
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1.
ORTEGA, Rafael & TARALLO, Massimo. Massera’s theorem for quasi-periodic differential equations. Topological Methods in Nonlinear Analysis [online]. 1 marzec 2002, T. 19, nr 1, s. 39–61. [udostępniono 22.7.2024].
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