$ _POST数组为空，我得到了未定义的变量错误

Okay, I practiced more on ajax - json - php and in the end this was my solution and my latest code.

Thanks for all answers and suggestions. Hope this also helps to someone.

Still open to any kind of advice to improve.

<?php

include('db.config.php');

if(isset($_POST['submit'])){


$name = addslashes($_POST['name']);
$email = addslashes($_POST['email']);
$address = addslashes($_POST['address']);
$income = addslashes($_POST['income']);
$amount_needed = addslashes($_POST['amount_needed']);
$phone = addslashes($_POST['phone']);

// process form as normal   

$sql = "INSERT INTO `" . DBN . "`.`creditapp` (`name`, `email`, `address`, `income`, `amount_needed`, `phone`) VALUES ('$name', '$email', '$address', '$income', '$amount_needed', '$phone')";
$db->Query($sql);

die();

<div class="container wrap wow fadeInUp">
     <div class="row">
     <div class="col-sm-5 col-md-6 left-app">
        <form id="form" action="creditapp.php" method="post">
          <input type="text" placeholder="Name" name="name" id="name" required>
          <input type="email" placeholder="Email"  name="email" id="email" required>
          <input type="text" placeholder="Address"  name="address" id="address" required>
          <input type="text" placeholder="Monthly income before taxes" id="income" name="income" required>
          <input type="text" placeholder="Amount Needed"  name="amount_needed" id="amount_needed" required>
          <input type="text" placeholder="Phone"  name="phone" id="phone" required>
        <div class="row">
        <div class="container">
          <input type="submit" name="submit" value="Submit" class="button sub"></div>
        </div>
        </form> 
        </div>

   <script>
   $(document).ready(function() {

   $('.sub').click(function(e){
       e.preventDefault();
        var name = $('#name').val(),
            email = $('#email').val(),
            address = $('#address').val(),
            income = $('#income').val(),
            amount_needed = $('#amount_needed').val(),
            phone = $('#phone').val();


        $.ajax({
            url: "creditapp.php",
            type: "POST",
            data: {
                name: name,
                email: email,
                address: address,
                income: income,
                amount_needed: amount_needed,
                phone: phone,
                submit: "submit"
            }

            }).done(function(msg){
              $('.right-info').html('<pre>' + msg + '</pre>');
            })
       })
   });
</script>

The problem you are having is with your javascript. You wait for the submit and than you do an ajax GET request, you need a POST.

<script>
            $(document).ready(function($) {
               'use strict';
            $('#form').submit(function(event) {  
               event.preventDefault();  
               var url = $(this).attr('action');  
               var datos = $(this).serialize();  
               $.post(url, datos, function(resultado) {  
               $('#result').html(resultado);  
               });  
           });
            </script>

Here is a simple Ajax call to a Php File by an event : Click on a button.

In your example you must use POST method because you use :

$_POST['something'];

Javascript client side :

 $("body").on("click", "#mybutton", function() {
            var mydata = $("#form").serialize();
            $.ajax({
                type: "POST",
                url: "/api/api.php",
                data: {data : mydata},
                timeout: 6e3,
                error: function(a, b) {
                    if ("timeout" == b) $("#err-timedout").slideDown("slow"); else {
                        $("#err-state").slideDown("slow");
                        $("#err-state").html("An error occurred: " + b);
                    }
                },
                success: function(a) {
                    var e = $.parseJSON(a);
                    if (true == e["success"]) {
                        $("#result").html(e['message']);
                        // here is what you want, callback Php response content in Html DOM
                    }
                }
            });
            return false;
        });

Next in your Php code simply do after any success function :

if ($result) {
            echo json_encode(array(
                'success' => true,
                'msg' => "Nice CallBack by Php sent to client Side by Ajax Call"
            ));
        }

You need to send a POST request for the $_POST array to have anything in it.

$.get(url, datos, function(resultado) {  
    $('#result').html(resultado);  
});

This sends a GET request (check $_GET). You want to use $.post here instead.

$.post(url, datos, function(resultado) {  
    $('#result').html(resultado);  
});