[see also: apart from, except]
Besides being very involved, the proof requires the use......
for no x besides the unique solution of......
[Note the difference between besides, except and apart from: besides usually “adds'' something, except “subtracts'', and apart from can be used in both senses; after no, nothing etc., all three can be used.]
[Do not write: “Besides, the solution is given by (5)'' if you mean: Moreover, the solution is given by (5).]