The servlet is mapped on an url-pattern of /greet, not /greetingservlet as you seem to expect as per the error message. So, change the URL in browser address bar accordingly. Also, the servlet class is declared to be Greetingapplication, but it has the actual name Greetingservlt. So, you need to align out the one or the other, otherwise Tomcat is unable to locate/load the servlet. Also, packageless servlet classes used to fail on some specific Tomcat + JVM combinations. To be on the safe side, you'd like to place the servlet class (as every other Java class) in a package (don't forget to update the web.xml accordingly).
There are more problems in the code posted as far, but they are as far not relevant to this particular question. Maybe in a new question.
