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The existence of periodic solutions to nonautonomous differential inclusions


Authors: Jack W. Macki, Paolo Nistri and Pietro Zecca
Journal: Proc. Amer. Math. Soc. 104 (1988), 840-844
MSC: Primary 34A60; Secondary 34A10, 34A25
MathSciNet review: 931741
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Abstract: For an $ m$-dimensional differential inclusion of the form

$\displaystyle \dot x \in A(t)x(t) + F[t,x(t)],$

with $ A$ and $ F$ $ T$-periodic in $ t$, we prove the existence of a nonconstant periodic solution. Our hypotheses require $ m$ to be odd, and require $ F$ to have different growth behavior for $ \left\vert x \right\vert$ small and $ \left\vert x \right\vert$ large (often the case in applications). The idea is to guarantee that the topological degree associated with the system has different values on two distinct neighborhoods of the origin.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0931741-X
Keywords: Periodic solution, differential inclusions
Article copyright: © Copyright 1988 American Mathematical Society