use strict;
use warnings;

my $user_input = "abc";
my $regex = qr/${user_input}_ABC_.*pd/;

foreach my $file  (qw (abc abc_ABC_something.pdf  abc_ABC_anything.pdf))
{   
   next unless $file =~ /$regex/;
   print "$file is valid\n";
}

__END__
abc_ABC_something.pdf is valid
abc_ABC_anything.pdf is valid