This question is dealt with in my book, Daniel, Prophet to the Nations (www.ipibooks.com). You definitely should get a copy! But… I better answer this question for you. In my book, I explain that in Daniel 11:2-35 the “kings of the North” are Seleucius and the Greek rulers who succeeded him (they ruled from Syria), and the “kings of the South” are Ptolemy and the Greek rulers who succeeded him (they ruled from Egypt). But the scene of the vision changes in Daniel 11:36-45 which is a prophecy about the final destruction of the Greek kingdoms–specifically of the Ptolemaic dynasty. In this case the king of the South is Egypt. Specifically it is Cleopatra and her ally Marc Antony. Cleopatra was the final Greek/Ptolemaic ruler. She and Marc Antony were defeated by Rome under Octavian at the Battle of Actium, which was both a naval and a ground campaign. So, in Daniel 11:36-45, the king of the North is Rome under Octavian. Rome will “extend his power over many countries; Egypt will not escape.” Because of the Battle of Actium (see my book), Rome also gained parts of Libya and Cush (Cush, not Ethiopia. Cush is lower Egypt). The facts of history line up perfectly with the prophecy in Daniel 11. Again, my book on Daniel will be helpful here.