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for questions involving inequalities, upper and lower bounds.

0 votes

Controlling solutions of a second order linear differential inequality

Wow, thank you for this detailed solution. I have a questions about case 1. You say $r'(x)=p_j(r(x)) = \rho_j^{-1}(r(x))$ where $\rho_j=r|_{I_j}$. In other words, if we restrict our attention to $I_ …
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4 votes
1 answer
514 views

Controlling subsolutions of a second order linear ODE

Also, any good references for differential inequalities that might help me solve this problem are equally welcome. …
6 votes
1 answer
2k views

Gronwall's inequality for higher order derivatives

Gronwall's inequality says that solutions to the initial value problem $u'(t) \leq \beta(t)u(t)$ with $u(0)=u_0$ are bounded by solutions to the problem with inequality replaced with equality for $t\i …