The universal bound property for a class of second order ODEs
Résumé
We consider the scalar second order ODE u + |u | α u + |u| β u = 0, where α, β are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 < α < β and moreover there is a constant C independent of the initial data such that ∀t > 0, u (t) 2 + |u(t)| β+2 ≤ C max{t − 2 α , t − (α+1)(β+2) β−α }.
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