how to check if web application already running?

Not sure what you mean.

The application (scope) only runs once.  A user cannot force another application scope to open up, ColdFusion controls this.  If no request is made within the timespan set for the application timeout, then the next request fires off the onApplicationStar() BIF automatically before the request BIFs are executed.

If you mean that you don't want them to have more than 1 browser open to the same website, I'm not sure that's going to cause any issues; as what was said before, the web is stateless.  ie:

If I open Chrome, and in Tab 1 I goto home.cfm and in Tab 2 I goto home.cfm the to ColdFusion, it basically sees 2 requests to home.cfm made from (in essence) the same person (even though it doesn't know that until you implement some form of user tracking).

But even if a person logs into a website, the session data is shared for the browser or session (depending in how your sessions are setup)  So even if he logs in on Tab 1, the next time he goes anywhere in Tab 2, it'll be when he's logged in.  The 2 tabs share the same session data.

Perhaps checking the client IP address or use Websocket.