Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I need some help please! Consider the following expression:

[itex]\left[1-\int_{x}^{1}F(\rho(\xi))f(\xi)d\xi\right]^{n-1} [/itex]

where [itex]F:[0,1]\rightarrow [0,1][/itex] is a continuously differentiable function with [itex]F'=f, x∈[0,1][/itex], and n>2. Suppose that [itex]\rho[/itex] belongs to the set of continuous and nondecreasing functions defined on [0,1]. Let C denote this set and endow it with the sup norm. I want to find a function [itex]\rho \in C[/itex] such that (with [itex]x<1[/itex] fixed):

[itex] \left[1-\int_{x}^{1}F(\rho^*(\xi))f(\xi)d\xi\right]^{n-1}\geq \left[1-\int_{x}^{1}F(\rho(\xi))f(\xi)d\xi\right]^{n-1}[/itex]

for all [itex]\rho \in C[/itex]. Does this make any sense at all? if so, how can be sure I can find this function?

Thank you so much for your help! I truly need it!

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# Sup of a Functional ?

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