Massera's theorem for quasi-periodic differential equations
Keywords
Bounded, recurrent and quasi-periodic solutions, partial differential equations on the torusAbstract
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.Downloads
Published
2002-03-01
How to Cite
1.
ORTEGA, Rafael and TARALLO, Massimo. Massera’s theorem for quasi-periodic differential equations. Topological Methods in Nonlinear Analysis. Online. 1 March 2002. Vol. 19, no. 1, pp. 39 - 61. [Accessed 29 March 2024].
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