Abstract

A method for computing bounds to periodic solutions of the system y 1=f(t, y), y,f∈R n, f periodic in t with period T, (1) is studied using an integral equation y=Gλy depending on a parameter λ, and whose solutions for each λ are the periodic solutions of (1). λ is then given a value λ 0 so as to determine a set S for which G λ 0 S ⊂ S. Since G λ 0 is proved to satisfy Schauder's conditions, then in S there is a solution of (2), i.e., a periodic solution of (1). The method, which evidently also constitutes an existence proof in S, has the peculiarity of being quite general since it can be used to bound other kinds of solutions of the system y′ = f( t, y), by simply setting up a different integral equation y = G λ y which possesses the solutions to be bounded. This method has then been used to bound periodic solutions of a system arising from the dynamics of two floating bodies, for which G λ S ⊂ S has the form of a system of inequalities.

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