First, please read How (Not) To Ask A Question, in particular the section on titles.

This is not a Perl issue, but an SQL issue. You can resolve this by using the IN operator.

As a side note, you should seriously consider using placeholders in your code. It will handle any character escaping that has to be performed and adds a layer of security. As an example, here is how you might form your $sql variable for finding all occurrences in your year array:

my $sql = "SELECT DISTINCT 
                               
                               name, email, addr, location
                               
               FROM            my_users
               WHERE           year IN (" . join(', ', ('?') x @year) 
+. ")
          ";
$i = 0;
my $query = $dbh->prepare($dbh) or die "Prepare failure: ".$dbh->errst
+r;
foreach my $year (@year) {
    $query->bind_param(++$i,$year);
}
$query->execute or die "Execute failure: ".$dbh->errstr;
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