i am researching my grandfathers family and have hit a brick wall with one part of it.

David Crosbie was born 1879 to Ellen Crosbie in Penninghame, Wigtown(scotland)

David married in 1898 and there was no father named on marriage cert just Ellen Crosbie with no maiden name supplied.

I am thinking she was an unmarried mother.
Have searched 1881 census and found a Ellen aged 17 living with family in Lancashire. She too was born in Wigtown (as was her family).
No mention of David.
I am now wondering if perhaps she gave him up for adoption.
If this is the case i have no idea where to begin.
Can anyone help me at all?
I am totally stuck.

thanks
amanda