Add a unique css class name to Aax action link
<h2 class="headstep2_1">@Ajax.ActionLink("Demat Details (CDSL)", "", "", new { ID = 99 }, new AjaxOptions { OnSuccess = " " }, new { @class = "uniqueclass floatleft LinkText" })</h2>
and then by using jquery you can change the text in button click event
$(document).ready(function(){
$('#buttonId').click(function(){
$(".uniqueclass").text("Your New Text")
});
});
Hope this helps