The dropdown is toggled with having the additional class 'open' added to the enclosing <li> element. So if you want to have it open on page loading:
<li class="dropdown open">
That will do the trick.
This little bit of jQuery script (I'm assuming you've loaded it becasue you're using Bootstrap) ought to do the trick. Once the DOM has loaded, it sends a click() to the dropdown toggle button.
$(document).ready(function () {
$("#posuvnik").click();
});
There is probably a way to do it in straight CSS, but without seeing more of your code it's hard to know.