Is my soon-to-be ex entitled to this house even though he has not contributed anything to this, not even with repairs?

Anything you buy during a marriage is marital property. Your husband must have signed something when you bought the house. Did you disclose to your lender that you were married. You have many problems wit any claim that the property is non-marital or that your husband has no claim. Any mortgage payments you made were made with marital funds. So why shouldn't get be entitled to something from the home.