I'm running Qtranslate for this site see: http://www.businessinstitute.nl/

I'm very astounded by this wordpress plugin. Now my only issue is which i cannot set a custom title and outline for my home page per language. I'm able to only setup one line for that title within the general configurations for this site.

I've installed Qtranslate META where I'm able to set a custom title and outline per page, but my only issue is the home page.

While you labeled PHP inside your question, this is a pure PHP method to address the "problem":

  1. You may make a static declaration in a wide array of all of the different translations for the website "title" as it is assumed this wont change that frequently, when...
  2. Determine when the user's browser is delivering an accept_language
  3. Present the particular title for the reason that user's language whether it is available inside your array
  4. Whether it does not exist, present a default language...

This is a quick implementation that's not determined by third party software / wordpress plugin:

 $website_titles = array ('en' => 'my cool website', 
                          'fr' => 'mon site cool',
                          'zn' => '我的酷网站');
 if (isset($_SERVER['HTTP_ACCEPT_LANGUAGE']) && isset($website_titles[$_SERVER['HTTP_ACCEPT_LANGUAGE']])) {
     echo '<title>' . $website_titles[$_SERVER['HTTP_ACCEPT_LANGUAGE']] . '</title>';
 } else { 
     // print default title
     echo '<title>my cool website</title>';
 }