soft shells in new layers

Hi
I have 3 young hens who came into lay for the first time about a week ago. The eggs have been great so far, but this morning we found one that had no shell, and at the other side of the box was the remnants of another that looked as if it had been eaten.
Is this common with hens coming into lay for the first time?
I'm feeding them layers pellets with corn as a regular treat, grit available at all times. They have a small run but roam around in a large fenced off area of the garden. I've tried giving them greens but they don't seem to bother with them.

Thanks for any advice you can give
Phil

Have they got oyster shell. I also put the egg shell in the oven for a couple of minutes then crush them down to very small pieces ( i find a rolling pin and a bowl does the job perfectly) then give it to the chickens and both of these will help to strenghthen the shell.Oyster shell should be avaliable all the time.