Properly indenting your code reveals the problem:

foreach(@urls)
{
        my $ua = LWP::UserAgent->new();
        my $url = "$_";
        my $response = $ua->head($url); #HTTP::Response type return
        my $headers  = $response->headers(); # HTTP::Headers type retu
+rn
        my $content_type =$headers->content_type(); # string
        print "$content_type\n";
}
if($content_type eq 'application/pdf')
{
        print "File Exists:\n $_";
}
elsif($content_type eq 'text/html')
{
        print "File Exists but requires subscription to access:\n";
}
else{
        print "No Matching found";
}
[download]

Your if is outside the loop, so the variable $content_type has gone out of scope, it's value is now undef.

Please use strict; use warnings;, that's a safeguard that catches such errors for you.

And indent your code properly, one indention level per opening curly brace. See perlstyle. As this example illustrates, it's not only a stylistic thing - it is essential for understanding the code.

Also please start by learning the basics of Perl. perlintro and the book "Learning Perl" are good places to start.