Certain semiconductor devices, under certain biasing condition (or in a certain mode), show the behavior that INCREASING the "signal" voltage across them causes REDUCTION in the current through them...Clearly, such a behavior (if it is linear enough) can be modelled by a negative resistance (current increases when voltage decreases).
Such devices are called negative resistance devices, and are very commonly used in oscillators.
However, I believe that the NEGATIVE RESISTANCE characteristic of the device itself has nothing to do with POSITIVE FEEDBACK, as some ppl replied (correct me if I'm wrong! - they are probably confused b/c +ve f/b is present in oscillators, however it has nothing to do with -ve resistance)....and such devices can operate in their "negative resistance mode" under proper biasing conditions, whether or not feedback is applied.
HOPE THIS HELPS!