In addition to what Fletch said, there are a few syntax errors I can point out:

All statements in Perl must end with a semicolon.

You need to use a string comparison operator (eq) instead of the assignment operator (=) in your if statement.

Using the strictures (use warnings; use strict;) will help avoid other common mistakes.

I think this is more like what you wanted:

#!/usr/bin/perl

use warnings;
use strict;

my $com1 = `ps -eaf | grep bpps | grep -v grep | awk '{print $1}'`;
my $com2;

if ($com1 eq 'weblogic') {
        print "bpps is running.\n";
} else {
        $com2 = `sh -c /export/home/weblogic/bai/bpps.sh start 2 > /de
+v/null 2>&1`;
}
[download]

This code is untested.