If you are a non resident and your income comes from outside the state most of the Lenders will give you a mortgage at a restricted LTV.
Eg
IIB , First Active , Ulster Bank , AIB will lend you a max of 80% of the value of the property assuming your salary can cover this amount
BOI, EBS and PTSB will lend you a max of 75% of the value of the property assuming your salary can cover this amount.
As far as I am aware , BOS and Leeds Buildings Society don't allow income form outside the state to be considered.
Most of the Lenders won't allow self certification for income coming from outside the state and will look for full 2/3 years trading accounts.
The likes of PTSB might, you'd have to provide full 3 months business bank statements and 3/6 months current accounts. The income you self certify would have to be reflected in the bank statements.