Both have and have got are used for possessions So, yes, these express the same meaning:
I have two brothers. / I've two brothers.
I have got two brothers. / I've got two brothers.
The verb have is used in many ways, including possession, whereas have got is only used for possession.
Check out these sites:
Have Got and Have - Possessive Forms in English for Beginning Level ESL EFL English Learners
BBC World Service | Learning English | Learn it
All the best.