Christophe

Just edit the "Home" page and change the "Title", which is the "navigation name" by default.
(You could redirect your homepage to the page you want.)
Please give more details.

Perhaps you'll find your solution here:
http://stackoverflow.com/questions/18890053/php-conditions-depending-on-window-width-media-queries
I guess there are "solutions" with PHP, PHP + Javascript, Javascript...
By the way, a ProcessWire version is missing at "3rd party modules" here: https://github.com/serbanghita/mobile-detect
NB: don't forget to also read the last answer(s).
Edit: see also https://css-tricks.com/forums/topic/how-to-load-a-section-of-content-only-if-the-screen-is-over-a-certain-width/

Hi,
(It's not a multilingual website.)
The mistery is solved. It's quite logical.
The language for Guest was Default. It had to be French to display the description when not logged in.
And the language for the superuser had to be French to display the description when logged in. I often changed the language for the superuser but I didn't notice the difference until now.
The multilingual description is deactivated by default so I hadn't realized that I had completed the "Description" (same label) only when logged in as the superuser with the French language.
I guess that if I had done the opposite it wouldn't have bothered, as the (empty) French description would have inherited from the Default one.
Thanks to both of you for helping me go more precisely in the right direction.

Hello,
Not sure I can help, and I don't know what you've already tried, but:
Have you read, for example, https://github.com/ryancramerdesign/ProcessWire#resolving-an-apache-500-error and/or http://processwire.com/docs/tutorials/troubleshooting-guide/
In site/config.php, have you customized this:
/**
 * Installer: HTTP Hosts Whitelist
 *
 */
$config->httpHosts = array('localhost', 'subdomain.name.tld/subdirectory/', 'othersubdomain.name.tld/');
Or this in .htaccess:
# -----------------------------------------------------------------------------------------------
  # OPTIONAL: Set a rewrite base if rewrites aren't working properly on your server.
  # And if your site directory starts with a "~" you will most likely have to use this.
  # -----------------------------------------------------------------------------------------------

  # RewriteBase /
  # RewriteBase /pw/
  # RewriteBase /~user/