First of all you can try to use the following command:
yum search libXext
Following this search you will find that you need to install the following library: libXext.i686 (or most probabily libXext.i386). After this you can run:
sudo yum install libXext.i686
As a side note, I needed also to install the following libraries in order to make my java application to work properly: libXrender.i686 and libXtst.i686. I think that this issue is due to the fact that we are trying to user a java 32bit version on a 64bit OS.
