Declare the variables in your Application class:

qx.Class.define("custom.Application",
{
  extend  : qx.application.Standalone,
  members :
  {
  /** My global variable */
   bGlobal : true
   main : function()
   {
  // access to global variable from within this class using "this"
     this.bGlobal = false;
   }
  }
}

Then you can access that main application class using qx.core.Init.getApplication() so in some other class, you can read the global like this:

qx.Class.define("custom.SomeArbitraryClass",
{
  extend  : qx.core.Object,
  construct : function()
  {
    /** Access the global variable */
    if(qx.core.Init.getApplication().bGlobal)
    {
      alert("The global is TRUE");
    }
  }
}

You could also have made that global be a property of the Application class:

qx.Class.define("custom.Application",
{
  extend  : qx.application.Standalone,
  properties :
  {
  /** My global variable */
   global : true
   ...

In which case you’d reference it from the other class using the property’s getter:

qx.core.Init.getApplicaiton().getGlobal()