JSFiddle - React, Tailwind, and code Playground
HTML
<input type="text" name="startdate" value="2016-04-08">
<input type="text" name="enddate" value="2016-09-02">
JavaScript
var inputStart = document.querySelector('[name="startdate"]');
var inputEnd = document.querySelector('[name="enddate"]');
var startDate = inputStart.value.split('-');
var endDate = inputEnd.value.split('-');
var startDateDay = parseInt(startDate[2], 10);
var endDateDay = parseInt(endDate[2], 10);
console.log(endDateDay >= startDateDay);