Aufgaben:Problem 14
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Revision as of 14:38, 26 December 2014 by Valentin (Talk | contribs) (Created page with "=Problem 4a= Let \( T > 0,\eta \in C^{1}([0,T]), \phi \in C^{0}([0,T]) \), and assume that: $$ \frac{d}{dt}\eta(t)<=\eta(t)\phi(t), \forall t \in [0,T] $$ Show that: $$\eta(t...")
Problem 4a
Let \( T > 0,\eta \in C^{1}([0,T]), \phi \in C^{0}([0,T]) \), and assume that: $$ \frac{d}{dt}\eta(t)<=\eta(t)\phi(t), \forall t \in [0,T] $$
Show that: $$\eta(t)<=\eta(0)e^{\int_{0}^{t} \phi(s) ds}, \forall t \in [0,T] $$
Hint: consider $$ \chi(t):= \eta(t) e^{-\int_{0}^{t} \phi(s) ds $$
