Dear Support,

I already found the solution, just a little failures: I forget the (jQuery) Endtag, so it never saw output something.. That’s also why no failure.

Final Soultion:

// Invoke jQuery
(function($){	
     //Load readyState	 	 
 	$(document).ready(function(){
            // Only apply to mainpage
            if ( $("#home_mainscreen").length) {
               //creates ajax search$
                new $.AviaAjaxSearch({scope:'#home_mainscreen'});   
            }
       }); 
  })( jQuery );

I hope these will help someone in the future :) if() check is optional if you include it permament.
Mark this thread as solved.
Greets Chris