I have a problem understanding the reasons as to why under some circumstances a term can be omitted due to it being a part of a bounded function, and I hoped to get some clarity to this here. There is of course a risk i'm completely amiss, but i would be very grateful for any insight given as to this topic of rules regarding bounded functions.
The specific problem i faced was solving the stationary temperature distribution of a sphere, where solving with the spherical Laplace operator $$-\dfrac1r \dfrac{d^2}{dr^2} \bigg(r\,u(r)\bigg) = q$$ left me with $u(r) = q\left(r^2/6 + A + B/r\right)$.
Now, the problem was solvable and matched the correct answer when assuming $u = q\ r^2/6 + A.$ But why is it that the $B/r$ term can be omitted in this context? All that was given was that the temperature has to be bounded inside the whole sphere, and I can't see how that term defies that.
Thanks,
Os