Authentication Required on my late husband's old ipad. I don't know the ID he used or his password. Is there any way to overcome this?

There is really no way around this. This is a security for all Apple devices in that the Apple ID that they are assigned to they stay assigned to until the owner removes them from their Apple ID. This is to keep unwanted users from gaining access to the device or to deter them from stealing.

You can try taking it to an Apple Store and explain the situation and bring them proof and they may do something to help you out. That is not a guarantee, however, that they will.