I found the solution which was all about the monitor settings. Hopefully, this will help other Apple users. I found it in the User's Guide, page 35. I skipped it earlier.
Thanks for posting.
Here is some information you may find helpful: http://dell.to/2vifRBD
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Thank you for trying to help, but I've already been there. I have emphasis in my original post (in bold) the main issue which is the monitor itself and not the mac.
I really need help from someone who knows this problem without sending me to various links as I googled for hours without finding a solution.
Have you tried the monitor with a Dell computer? Does it produce the same results as you are describing?
Unfortunately we have only done minimal testing with Mac products for obvious reasons so our research is limited.
I'm very disturbed now. I read about this screen in many places. I don't have Dell computer and (in my opionion) I think Dell has to make these kind of test with Apple hardware and software. I will try to see if I can get a refund for it since it is not fitting to my needs.
Thanks for posting the solution so others can find it.