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Une remarque sur les solutions bornées d’une équation différentielle avec pilotage. (French) Zbl 0612.34060

Under suitable hypotheses on f, for some bounded function \(u\in C^ 1({\mathbb{R}}^ 2)\) it is proved that every solution y(t) of the differential equation \(y'(t)=f(t,y(t),u(t))\) with \(| y(0)| <k\), for a contant \(k>0\), satisfies \(| y(t)| <k\) in \(0\leq t<\infty\). An application is included.

MSC:

34H05 Control problems involving ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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