It WORKS !
Thanks a million, I really appreciate the help.
For the convenience of others, the final code: this displays in the div only the available language(s), and no div if there is no translation available.
<?php
$switcher = pll_the_languages( array(
'show_flags'=>1,
'show_names'=>1,
'force_home'=>0,
'hide_if_no_translation'=>1,
'hide_current'=>1,
'echo' => 0
) );
if($switcher): ?>
<div id="LanguageSwitcher" class="styleLanguageSwitcher" >
<ul><?php echo $switcher ?></ul>
</div>
<?php endif; ?>