[This question](https://physics.stackexchange.com/questions/137171/lsz-reduction-vs-adiabatic-hypothesis-in-perburbative-calculation-of-interacting) is a math question.
It may use equations which are commonly found in physics, and it may refer to non-linear terms as "interactions", but the question itself is purely about math.
It was not put on hold or marked as off-topic.

Here's [another purely math question](https://physics.stackexchange.com/questions/137131/evaluate-langle-mathbfp-1-hatr-mathbfp-rangle) which was not put on hold.

On the other hand [this question](https://physics.stackexchange.com/questions/137121/how-is-the-method-of-lagrange-multipliers-used-for-multiple-constraints-of-multi), which is also a math question, was put on hold as off-topic.
The difference in this latter question is that the asker focused directly onto the mathematics, stripping away whatever physics may have been at hand in when they identified the mathematical problem at the heart of the issue.

The difference between these questions is cosmetic.
There is no substantive reason to consider the first or second questions "physics" other than the fact that the math questions represented there was encountered in a physics textbook.
For all we know, the same may be true for the latter question, and is in fact likely given that the asker came here rather than to the math SE.

Why do you think one of these questions was put on hold while the other was not?

P.S. I think the answer is pretty obviously that there are more users here who are familiar with the math relevant to the first two questions than the third.
Is this a good reason to close the third question?