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First of all, I apologize for asking this question if the topic has already been debated on the MO.meta, but I did not succeed in finding anything similar: and now the question.

Nearly a year ago I noticed this question, I liked it and consequently upvoted it and started to investigate if it was possible to give a good answer. I worked to this almost from that day up till two weeks ago, when I thought found a nice answer, precisely this one: however, after posting it with many editing cares, I reread the original question and it appeared evident to me that I did not answered it!

Precisely, as Bob Terrel pointed out in is early posted comment to the question, $$ \int f(y,\alpha)f(y-x,\alpha)\mathrm{d}y\neq \int f(y,\alpha)f(x-y,\alpha)\mathrm{d}y $$ i.e. nonlinear the integral operator in equation $(\ast)$ of the original question is not of convolution type. I thought to remove completely my answer but, considering the commitment that I lavished in it, I am not sure this is a good idea, since

  1. Even the equation studied is not the proposed one, I succeeded in proving the existence, uniqueness and regularity (respect to the spatial variable $x\in \Bbb R^n$) of the Cauchy problem for a nonlinear integrodifferential equation for large classes of Cauchy data. And even if the original problem is perhaps more difficult, this one is non trivial, at least when dealing with it in a non formal way.
  2. Some of the remarks and references to the Division problem in its most general form proved by Łojasiewicz maybe useful to someone per se, since it is not usually presented in this form.

I thus decided to ask for advice here on meta: what should I do with it? Below I propose some viable alternatives, not all mutually exclusive:

  • I could simply remove it.
  • I could edit it at the top by adding a brief explanation on why it is not an answer.
  • I could remove it as answer to the specific question, ask a fitted question and then post it as a this time appropriate answer to it.
  • I could go out with friends more frequently, so when I'll came home I'll be more relaxed and focused on the solution of the problem posed on the MathOverflow, without bothering other members.
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    $\begingroup$ I have often left erroneous posts with words added at top indicating the nature of the error. Sometimes it was to indicate what happens if you misread the question, and other times it was a warning to others as to what happens when you take the wrong path. If people can learn from the post and the question together, you can leave the post up. Gerhard "In My Rather Unhumble Opinion" Paseman, 2019.02.15. $\endgroup$ – Gerhard Paseman Feb 16 at 2:51
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    $\begingroup$ in this particular case it was the question itself which was improperly phrased (the title did not match the content); the answer has upvotes, it serves a purpose. $\endgroup$ – Carlo Beenakker Feb 16 at 19:36

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