I received a pop up message my iPhone5 is infected with a Trojan

Hi,

I went to Google through Safari and was doing a web search when I received a message that popped up the iPhone was infected with a Trojan. The message said click here to scan but I didn't do that. I pressed the button on the phone to bring me back to the desk top and then I went to Settings to clear history and cookies and data. A few days ago I received a message that’s aid I needed to confirm my password for Yahoo. I canceled and the message came up today. I entered an incorrect password hoping that I would receive a message back that said the password was incorrect. However, the screen cleared as if I had given the correct password. Another thing that started to happen is the phone powers down and won’t power up. I have to connect the USB cable to a PC to get it to power up again. I started to worry that there is a Trojan on my iPhone5. Has this ever happened to anyone? I read articles that said it is impossible to get a virus on the iPhone but I don’t know if that is accurate. I know there isn’t any antivirus that can scan the iPhone but is there a way to check it to see if it is infected?

Thanks!