Solution 1:

Both are used. This is an area of controversy where no 'correct' way has been established. Some sources would say that Oliver Twist is Dickens' character while other sources (like Strunk & White) would say that he is Dickens's character. See this page for a brief exploration of some of the rules different sources use in different situations.

It's probably safest to stick with the 's ending unless it would make the pronunciation awkward or violate historical usage. For instance, you would want to write Achilles' heel, not Achilles's heel.