Seeking solution for Civilization V war on island problem



I would ask if others who may play of the Civilization V game could help me to solve problems I am having in waging war.

On nation city formed on small island, sometimes single hex area, how do I defeat them effectively?

I have Battleships but they do not seem able to defeat it by themselves. I try amphibious unit to attack on sides and again it appears to seem ineffective.

On land with access from many sides I can send infantry on all sides and attack in rotation and it will defeat, but single island nations are not working.

Can someone provide good solution for this problem?

Thank you for helping.