Cut them off and apply roundup to the stump with a paintbrush. Be sure to get the liquid on the outermost edge of the trunk - that is the living layer, not the center of the stump.

They are probably small shrubs at this point, maybe tens of thousands of them, right?
Trying to apply dabs of liquid on that many gets to be impossible. I had the same situation ten years ago. The solution for me was to chop them down, then spray with concentrated 2-4-d in the Spring when the leaves are sprouting. It will take a long time to eradicate them all. Perhaps 50 years !!!

Agreed with the above posters. Don't be discouraged, break it down into sections and give yourself small, achievable goals.

I have been battling 2 species of Buckthorn in the back of my lot for about 6 years. The Glossy Buckthorn (Frangula alnus) is the worst. Because the roots are very strong, it is difficult to dig out, and even my medium sized weed wrench doesn't work easily on specimens over 1 inch diameter.

Similarly to what the other posters have said, herbicides work best to control this plant. For large specimens, I cut them down at the base and apply concentrated herbicide to the cut stump. I use a squeeze bottle of Brush-b-gone concentrate (or other stump killer) and apply as quickly as possible after cutting.

For smaller specimens, I've discovered that Brush-b-gone solution works very well when sprayed on the foliage during the growing season.

Steelskies, should you still be around, I'd like to add a comment or two. First, the cut-and-apply-herbicide treatment is very legitimate but is for larger stems. The glyphosate to be used should be at a 50% concentration, far stronger than is normally used to spray the foliage of undesired plants. Another chem. called Garlon can be helpful too, though I usually stick to glyphosate. Also, this should be done in late summer/early fall.

Young buckthorns, and by this I do mean seedlings, actually pull out of the ground readily. It's actually kind of fun to pull these b*stards out, though the fun wears off after the first 1000.

Finally, if you are dealing with mature specimens, be very wary of how you drag them out of your area. If there's lots of fruit, you could be spreading the plant around without knowing it.

Good luck. It's definitely a tough battle. Usually, even when an area has been completely eradicated, there are usually viable seeds already in the ground which will soon sprout.

+oM