I'm really having a hard time finding a book that covers distributional equations such as $xT = \delta(x)$ or distributional differential equations. Any suggestions?



Distributional equations: reference request
This is the problem of division of distributions. The general existence theorem is the Malgrange-Ehrenpreis Theorem. The first two volumes of Hörmander's "The Analysis of Linear Partial Differential Operators" is a canonical reference. See also [this book](http://link.springer.com/book/10.1007/978-3-319-20140-5) by Ortner and Wagner.


