can i get the list of items between two date like ?
var startDate.
var EndDate.
var queryGetDiscussion = "?$Date between(startDate, EndDate) ";
Or using LT and GT.
Under the assumption that you are asking about the SP2013 REST API.
Yes, but you would have to perform a few more conversions/comparisions like day(), month(), year() manually.
The oData Query Operators supported by SharePoint REST Api are listed here: http://msdn.microsoft.com/en-us/library/fp142385.aspx