A non well formed numeric value encountered

Question

Because you are passing a string as the second argument to the date function, which should be an integer.

string date ( string $format [, int $timestamp = time() ] )

Try strtotime which will Parse about any English textual datetime description into a Unix timestamp (integer):

date("d", strtotime($_GET['start_date']));

$_GET['start_date'] is not numeric is my bet, but an date format not supported by strtotime. You will need to re-format the date to a workable format for strtotime or use combination of explode/mktime.

I could add you an example if you'd be kind enough to post the format you currently receive.

This error occurs when you perform calculations with variables that use letters combined with numbers (alphanumeric), for example 24kb, 886ab ...

I had the error in the following function

function get_config_bytes($val) {
    $val = trim($val);
    $last = strtolower($val[strlen($val)-1]);       
    switch($last) {
        case 'g':
            $val *= 1024;
        case 'm':
            $val *= 1024;
        case 'k':
            $val *= 1024;
    }
    return $this->fix_integer_overflow($val);
}

The application uploads images but it didn't work, it showed the following warning:

Solution: The intval() function extracts the integer value of a variable with alphanumeric data and creates a new variable with the same value but converted to an integer with the intval() function. Here is the code:

function get_config_bytes($val) {
    $val = trim($val);
    $last = strtolower($val[strlen($val)-1]);
    $intval = intval(trim($val));
    switch($last) {
        case 'g':
            $intval *= 1024;
        case 'm':
            $intval *= 1024;
        case 'k':
            $intval *= 1024;
    }
    return $this->fix_integer_overflow($intval);
}

The function fix_integer_overflow

// Fix for overflowing signed 32 bit integers,
// works for sizes up to 2^32-1 bytes (4 GiB - 1):
protected function fix_integer_overflow($size) {
    if ($size < 0) {
        $size += 2.0 * (PHP_INT_MAX + 1);
    }
    return $size;
}

I ran into this same situation (in my case with a date value in a custom PHP field in a Drupal view), and what worked for me was using intval instead of strtotime to turn the value into an integer - because it basically was a timestamp, but in the form of a string rather than an integer. Obviously that won't be the case for everyone, but it might be worth a try.