Search for a file in specific directory

I have to search a file in a prticular directory. filename will be passed through command line. The directory may contain subdirectory.

i.e.
suppose directory in /u03/appl (it can hard coded in script). This directory may contain subdirectory.

$ scriptname.sh filename

output should be file name if it is there in directory tree.

i've tried some thing but didn't get success. Please help me out
below is code that i had tried

#!/bin/bash
echo $1
if test $# -eq 0 ; then
  echo usage: "${0##/*} [Dir name]"
  exit
fi
echo 'Search in directory /u03/appl for the $1'
for arg in $* ; do
  #if test -e $arg ; then
  files=$(ls -lR /u03/appl | grep '[^d]' | awk '{print $9}') # <=
  for file in $files ; do
    if [[ $1 = $file ]]
    then
      echo 'got it'
    else
      echo 'try again'
    fi
done
#echo $files
#fi
done
#End

Why doesn't the following work

cd /u03/appl
find ./ -name $1 -print

It will fail if $1 contains whitespace.

find /u03/appl -type f -name "$1"