My adoptive boys each have special needs. Then it asks if they are 'disabled'. How do I determine if they are considered to be disabled?

Here are the IRS qualifications to determine if a qualifying child is permanently and totally disabled.  Both of the following must apply:

1. He or she cannot engage in any substantial gainful activity because of a physical or mental condition and
2. A doctor determines the condition has lasted or can be expected to last continuously for at least a year or can lead to death.

Additionally you will need to keep for your records, proof of permanent and total disability in the form of a letter from the child’s doctor, other healthcare provider or any social service program or agency verifying the child is permanently and totally disabled. 

Here is a link with more details on the subject.