# X' > -X +A(t) - \int_{0}^{t}{b(X(u)) du} (help on a integrodifferential inequality)

Discussion in 'Math Research' started by Arboristeria, Sep 17, 2005.

1. ### ArboristeriaGuest

Dear All,
let us consider the follwing integrodifferential inequality:

X' > -X +A(t) - \int_{0}^{t}{b(X(u)) du}
X(0)=q

with

A(t) continuous
b(w) positive and increasing.

At the best of your knowledge (*), are there conditions on A(t)
and/or b such that, if they were fullfilled, it may be:

X(t) > Y(t)

where Y(t) is the solution of

Y' = -Y +A(t) - \int_{0}^{t}{b(Y(u)) du}
Y(0)= q

?

Do you know (*) if there is some book or review paper on the topic
"integrodifferential inequalities" ? I was able only to find a book on
integral inequalities (by simeonov and bainov), which contains a
chapter on integrodifferential inequalities.

Thank you very much and sorry for my bad english !

Ciao from

Arbore II

---
(*) Please answer to this post only if you have a pcecise answer and
not like: "Well, you you search with www.googeleinequalities.com you
might find something.. " or " maybe in the book 'inequalities for
dummies' maybe there is a chapter or maybe not..." or "try to write to
prof XY at swedish academy of sciences..." Arboristeria, Sep 17, 2005

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