Is my child entitled to child support

by Tamika
(San Pedro Sula,Honduras)

I am from Honduras and I have a child that was born here but the father is a US citizen enlisted in the US army. He went back to the US before the child was born so his name is not on the birth certificate. Sometimes he contacts the child and had sent money about 5 times since the child was born, the child is now 10 yrs., but he has never seen the child because he is married and choose not to. Listening to my situation, can I claim child support for my child?