Not only is it permitted, it is actively encouraged.
As the founder of Stack Exchange, Jeff Atwood, said long ago:
I do it all the time! For example, when I ran into a nasty issue with Java exploits in Google Chrome when browsing for images, I documented that on Super User by asking and answering my own question. Now, others can benefit from my ...
If you had a problem with a Web Application that you solved and you think that it would benefit other users then please do post the question and answer.
You can even post the answer at the same time as the question.
However, if this is your web application then you are potentially skating on thin ice/sailing close to the wind (pick your metaphor) as regard ...