I cannot compare dates with Datetime() in PHP

Question

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 at the part of the comparison it does not occur, the result should be the display of an error message because the date that the form sends is less than the date that is in the variable $range_start, someone can 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'];
        }
    }
?>