For an m-dimensional differential inclusion of the for;…#x220A;A(t)x(t;…[t, x(t)], wit;…n;…-periodic in t, we prove the existence o;…onconstant periodic solution. Our hypotheses requir;…o be odd, and requir;…o have different growth behavior for |x| small and |x| 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.
The existence of periodic solutions to nonautonomous differential inclusions / J. Macki; P. Nistri; P. Zecca. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 104:(1988), pp. 840-844. [10.1090/S0002-9939-1988-0931741-X]
The existence of periodic solutions to nonautonomous differential inclusions
NISTRI, PAOLO;ZECCA, PIETRO
1988
Abstract
For an m-dimensional differential inclusion of the for;…#x220A;A(t)x(t;…[t, x(t)], wit;…n;…-periodic in t, we prove the existence o;…onconstant periodic solution. Our hypotheses requir;…o be odd, and requir;…o have different growth behavior for |x| small and |x| 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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