Is there any way to check if an element has jquery select2 already applied to it?

Working solution:

$('.MyDripdowns:not([class^="select2"])').each(function (i, obj) {
    $(obj).select2({width: "455px"});
})

Links:

1. ^= attribute starts with selector
2. :not selector

you can check if the element has select2 attribute

$('.MyDripdowns').each(function (i, obj) {
    if (!$(obj).data('select2'))
    {
        $(obj).select2({ width: "455px" });
    }
});

EDIT

As @Fr0zenFyr said in his comment for v4.0 you can use :

if (!$(obj).hasClass("select2-hidden-accessible"))

Above answer is almost correct.
But it creates problem when we are adding elements dynamically on same page and applying select 2 to newly created element.
At that times selector has to be specified using not only class but also with input type. PFB reference code.

$('inputp[type="text"].MyDripdowns').each(curr_idx, curr_elem){
    //Check if select 2 is already applied or not
    if($(curr_elem).hasClass('.select2-offscreen')){
      //Select 2 is already applied to this element
    }
    else{
       //Apply Select 2 to this element 
    }
}