I would like to know when (for what functions $f$) and how I can find integrable solution of equation \begin{align} f(x)=\int_x^{\infty}\frac{u(y)}{\sqrt{y-x}} \ dy, \end{align} where $u$ is unknown function?
Thanks.
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Hello and welcome to MSE. Consider adding some more context/background on what you already know, or any work you've tried (if anything) to assist those here in helping you. – Adam Hughes Mar 19 '15 at 23:16
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You need some conditions on the function $u$. – science Mar 20 '15 at 02:42
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What kind of conditions on $u$ are useful in knowing a solution exists? – patric Mar 20 '15 at 09:25
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@patric, perhaps my question and solution might be relevant to you, see https://math.stackexchange.com/questions/3757692/help-with-variant-of-abels-integral – pdini Jul 18 '20 at 10:55