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. Arboristeria

    Arboristeria Guest

    Dear All,
    let us consider the follwing integrodifferential inequality:

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


    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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