尝试一下:

var date = DateTime.ParseExact("20120214", 
                              "yyyyMMdd", 
                               CultureInfo.InvariantCulture);    

var result = dbContext.orders
        .Where(q => dbContext.orders
                     .Where(s => s.purch_amt < q.purch_amt)
                     .Where(s => s.ord_date == date).Count() > 0)
        .ToList()