#! /usr/bin/perl
use strict;
use warnings;
use DBI;

my $dbname = 'schueler.db';

my $dbh = DBI->connect(
    "dbi:SQLite:dbname=$dbname",
    "", # empty user
    "", # empty password
    {
        RaiseError => 1,
    },
) or die $DBI::errstr, "\n";

# see http://search.cpan.org/perldoc?DBI#selectrow_array
# no "or die..." here, because empty list may be returned 
# which would trigger the "or die"... Remember, that 
# RaiseError is enabled above!
my @row = $dbh->selectrow_array(
  q~SELECT name FROM sqlite_master WHERE name='schueler'~,
);

if ( ! @row ) {
    # Table 'schueler' does not exist

}

__END__