I can not compare dates with DateTime () in PHP

I have a form where I send the date 1-4-2017 in each separate field (day, month and year). The code below receives the date normally, but when it arrives in the comparison part it does not occur, the result should be the display of an error message because the date the form sends is less than the date that is in the $range_start variable %, can someone help me?

<?php

    //cria um objeto datetime para seis meses atrás
    $range_start = new DateTime("6 months ago");

    //cria um objeto DateTime para hoje
    $range_end = new DateTime();

    //há um ano de quatro dígitos em $_POST['year']
    $input['day'] = filter_input(INPUT_POST, 'day', FILTER_VALIDATE_INT, array('options'=>array('min_range'=>1, 'max_range'=>31)));
    $input['month'] = filter_input(INPUT_POST, 'month', FILTER_VALIDATE_INT, array('options'=>array('min_range'=>1, 'max_range'=>12)));
    $input['year'] = filter_input(INPUT_POST, 'year', FILTER_VALIDATE_INT, array('options'=>array('min_range'=>1900, 'max_range'=>2100)));

    print $input['year'].'-'.$input['month'].'-'.$input['day'];

    if($input['year'] && $input['month'] && $input['day'] && checkdate($input['month'], $input['day'], $input['year'])){
        $submitted_date = new DateTime($input['year'].'-'.$input['month'].'-'.$input['day']);
       print "<br/>".$submitted_date->format("Y-m-d");
        if(($range_start> $submitted_date)||($range_end< $submitted_date)){
            $errors[] = 'Please choose a date less than six months old.';
        }
    }else{
        $errors[] = 'Please enter a valid date';
    }

    if($erros){
        foreach($errors as $msg){
            print $msg."\n".$input['day'];
        }
    }
?>