Inequality of ODE












3














Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.






differential-equations







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  • 2




    $frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
    – Cesareo
    6 hours ago


















3














Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.






differential-equations







share|cite|improve this question


















  • 2




    $frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
    – Cesareo
    6 hours ago
















3












3








3


2





Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.






differential-equations







share|cite|improve this question













Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.






differential-equations




differential-equations






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asked 9 hours ago









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  • 2




    $frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
    – Cesareo
    6 hours ago
















  • 2




    $frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
    – Cesareo
    6 hours ago










2




2




$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago






$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago












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