Your question is confusing. To answer your question, No, you cannot, by definition, write to an InputStream. InputStreams can only be read.
Your explanation of what you want to do gives me a clue, but isn't detailed enough for me to do more than guess. And that guess is that you want to read the input, conditionally perform processing depending on that output, then send the results of that processing to a JSP for display. In other words, you don't want to pass streams around, just chunks of data. If this is the case, you want to do the following after you process your data in the servlet:
Then, in your "DisplayResults.jsp", do this to get the data back out:
Then just access the Results
string like you would any variable in a JSP. What this amounts to is treating the HttpServletRequest as a Hashtable you can store data in, then pass it on to the next Servlet (use relative path to Servlet) or JSP for more processing or for display.
Hope this is what you were looking for. If you're new to Servlets and JSPs, I highly recommend buying "Special Edition using
Java Server Pages and Servlets". It covers both quite well individually as well as how best to get them to work together. Instead of just using it as reference, I actually started reading it (skimming a little here and there) and learned tons, which completely changed the way I did things and made my work much less frustrating.
Hope this helps!