Hi,
Try this once for get results
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
<script src="Scripts/jquery-1.4.1-vsdoc.js" type="text/javascript"></script>
<script src="Scripts/jquery-1.4.1.js" type="text/javascript"></script>
<script language ="javascript" >
function f1(tid) {
$("#searchdiv").load("searchpage.aspx?action=get", {searchitem:tid.Value}, function (data) { });
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<input type ="text" id="txtsearch" onkeyup="f1(this)" />
<div id="searchdiv">
</div>
</div>
</form>
</body>
</html>
here you've to write your search code in pageload of searchpage between querystring condition .
All the best