I thik it is kind of clear to me that of 50%+1 attack, but now i am thinking about something that occurred when i was testing a DAPP in a two node network. Each node had a blockchain (the same blockchain) with about 7000+ blocks (they both had equal number of blocks). I was using go-ethereum (GETH). Then i stopped the proccess, ran it again, and connected the two nodes, when i check the number of blocks on each of them, it was twice the number before (14000+). So, it is clear to me that the valid blockchain is the one present in 50%+1 of nodes of the network. But, what happens when 50% of the network has a different blockchain (both blockchains could be valid)?
When one speaks about 50%+1 attack, this usually has nothing to do with majority of nodes. Actually, it is quite cheap to control the majority of nodes, but this will not give any advantage to the one who controls it.
50%+1 attack is about controlling the majority of mining hash power in blockchains based on proof-of-work consensus alogithms. Well known examples of such blockchains are Bitcoin and Ethereum mainnet.
The one who controls the majority of hash power may successfully undertake various attacks on other blockchain users. The most known such attack is based on the ability to roll back transactions, that are considered finalized by other users. So, the attacker may transfer his cryptocurrency to a merchant in exchange for some goods or services, receive these goods or services, and then use 50%+1 of hash power to roll back the original cyptocurrency transfer.