PHILADELPHIA — The children typically show up at hospitals scattered across the country, one or two at a time, with symptoms like unexplained vomiting, diarrhea and jaundice. These are the classic signs of hepatitis — inflammation of the liver — yet in many cases, no cause is ever identified. That’s why the nation’s disease detectives are so intrigued by the evidence emerging from more than 200 pediatric hepatitis cases dating back to October, including a handful from Pennsylvania, New Jersey, and Delaware. Close to half of the children, including an initial nine identified in Alabama, tested positive for an adenovirus — a type of virus not normally associated with hepatitis. It’s possible that the virus has been responsible all along for many of the cases for which no cause is ever identified, CDC officials said at a briefing.