There
is an
upper mass limit for brown dwarfs, because above this limit the object is driven by nuclear fusion reactions; for an object of over 0.08 solar masses, the temperature of the core is hot enough to initiate hydrogen fusion reactions.
But there is really
no lower mass limit for brown dwarfs, as they don't have long-term self-sustaining nuclear reactions to keep them hot, so they just gradually cool off. For objects of under about 0.07 times the mass of our Sun, these objects simply cool and fade, and likely they also shrink a lot.
It is for this reason that Jupiter is sometimes called "a failed star"
Free floating (= not associated with a planetary system or star) objects have been found near the Orion Nebula that are actually less than 1 percent of the mass of our own Sun;
in other words, these objects , each of them less massive than 10 Jupiters, could be thought of as either planets or brown dwarfs.
Brown dwarfs are exceedingly low in luminosity (= actual energy output), which is why they were first observed only late in the history of 20th C. astronomy! The faintest-known actual
stars , have about
1/150,000 of the energy output of our own Sun (as measured in the visual bandpass), and brown dwarfs can get much fainter than this!
A comprehensive, up-to-date, but difficult to read, discussion of the mass distribution (mass function) of low mass stars and of brown dwarfs, is in this paper:
http://arxiv.org/pdf/1205.2966v1.pdf
Oh, and incidentally, the Sun is not a "typical" star, because the
most numerous stars are actually tiny faint things with only 0.2 to 0.3 times the mass of the Sun.
