can i request alimoney,if my husband abandoned the home and has a live in girlfriend now

you can always request alimony, and the court will consider all the circumstances such as his income and the conduct of both parties that led to the separation. there is no guarantee you would be entitled to it, but it sounds like you have a good argument. the question will be how much "other income" does he have. if you haven't already, a lawyer will help you file for divorce and request alimony from him. you can schedule a hearing in front of a judge to determine whether he will have to pay.