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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
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