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Une remarque sur une évaluation des solutions bornées d’une équation différentielle avec pilotage. (French) Zbl 0744.93054
For given functions $$a(t)$$ and $$b(t)$$ of class $$C^ 1$$ the author constructs an pilotage $$\{u_ 1(t),u_ 2(t)\}$$ such that for each solution $$x(t)$$ of the equation $x'(t)=f(t,x_ t,u_ 1,u_ 2),\quad t>0\qquad (x_ t(\theta)=x(t+\theta), -1\leq\theta\leq 0)$ with initial conditions of the form $$b(0)\leq x(t)\leq a(0)$$ for $$-1\leq t\leq 0$$ and the pilotage $$\{u_ 1,u_ 2\}$$ the property $$b(t)\leq x(t)\leq a(t)$$ for $$0\leq t<+\infty$$ holds. The method applied bases on the method of successive approximations.
##### MSC:
 93C25 Control/observation systems in abstract spaces 34C11 Growth and boundedness of solutions to ordinary differential equations 93C15 Control/observation systems governed by ordinary differential equations
##### Keywords:
pilotage; successive approximations
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