Holass samigos, acá les dejo el script que uso para iniciar geoserver, lo ponen el /etc/init.d y luego corren el comando:

update-rc.d geoserver defaults

Espero les sirva.

#! /bin/sh
### BEGIN INIT INFO
# Provides:          geoserver
# Required-Start:    $local_fs $remote_fs
# Required-Stop:     $local_fs $remote_fs
# Default-Start:     2 3 4 5
# Default-Stop:      0 1 6
# Short-Description: GeoServer OGC server
### END INIT INFO

# Author: Lennart Juette

# Geoserver configuration - use /etc/default/geoserver to override these vars
# user that shall run GeoServer
USER=root
GEOSERVER_HOME=/opt/geoserver-2.0.3
GEOSERVER_DATA_DIR=$GEOSERVER_HOME/data_dir

PATH=/usr/sbin:/usr/bin:/sbin:/bin
DESC="GeoServer daemon"
NAME=geoserver
JAVA_HOME=/usr/lib/jvm/java-6-openjdk/jre
JAVA_OPTS="-Xms128m -Xmx512m"
DAEMON="$JAVA_HOME/bin/java"
PIDFILE=/var/run/$NAME.pid
SCRIPTNAME=/etc/init.d/$NAME

# Read configuration variable file if it is present
[ -r /etc/default/$NAME ] && . /etc/default/$NAME

DAEMON_ARGS="$JAVA_OPTS $DEBUG_OPTS -DGEOSERVER_DATA_DIR=$GEOSERVER_DATA_DIR -Djava.awt.headless=true -jar start.jar"

# Load the VERBOSE setting and other rcS variables
[ -f /etc/default/rcS ] && . /etc/default/rcS

# Define LSB log_* functions.
# Depend on lsb-base (>= 3.0-6) to ensure that this file is present.
. /lib/lsb/init-functions

do_start(){

	# Return
	#   0 if daemon has been started
	#   1 if daemon was already running
	#   2 if daemon could not be started

	start-stop-daemon --start --pidfile $PIDFILE --make-pidfile \
		--chuid $USER --chdir $GEOSERVER_HOME \
		-b --test --exec $DAEMON -- $DAEMON_ARGS > /dev/null \
		|| return 1

	start-stop-daemon --start --pidfile $PIDFILE --make-pidfile \
		--chuid $USER --chdir $GEOSERVER_HOME \
		-b --exec $DAEMON -- $DAEMON_ARGS \
		|| return 2
}

do_stop(){

	# Return
	#   0 if daemon has been stopped
	#   1 if daemon was already stopped
	#   2 if daemon could not be stopped
	#   other if a failure occurred

	start-stop-daemon --stop --pidfile  $PIDFILE \
		--user $USER \
		--retry=TERM/30/KILL/5

	RETVAL="$?"
	[ "$RETVAL" = 2 ] && return 2

	# Many daemons don't delete their pidfiles when they exit.
	rm -f $PIDFILE
	return "$RETVAL"

}

case "$1" in
  start)
	[ "$VERBOSE" != no ] && log_daemon_msg "Starting $DESC" "$NAME"
	do_start
	case "$?" in
		0|1) [ "$VERBOSE" != no ] && log_end_msg 0 ;;
		2) [ "$VERBOSE" != no ] && log_end_msg 1 ;;
	esac
	;;
  stop)
	[ "$VERBOSE" != no ] && log_daemon_msg "Stopping $DESC" "$NAME"
	do_stop
	case "$?" in
		0|1) [ "$VERBOSE" != no ] && log_end_msg 0 ;;
		2) [ "$VERBOSE" != no ] && log_end_msg 1 ;;
	esac
	;;
  restart|force-reload)
	log_daemon_msg "Restarting $DESC" "$NAME"
	do_stop
	case "$?" in
	  0|1)
		do_start
		case "$?" in
			0) log_end_msg 0 ;;
			1) log_end_msg 1 ;; # Old process is still running
			*) log_end_msg 1 ;; # Failed to start
		esac
		;;
	  *)
	  	# Failed to stop
		log_end_msg 1
		;;
	esac
	;;
  *)
	#echo "Usage: $SCRIPTNAME {start|stop|restart|reload|force-reload}" >&2
	echo "Usage: $SCRIPTNAME {start|stop|restart|force-reload}" >&2
	exit 3
	;;
esac

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