[jsf-2] How to use if, else condition in jsf to display image

It is illegal to nest EL expressions: you should inline them. Using JSTL is perfectly valid in your situation. Correcting the mistake, you'll make the code working:

<html xmlns="http://www.w3.org/1999/xhtml" xmlns:c="http://java.sun.com/jstl/core">
    <c:if test="#{not empty user or user.userId eq 0}">
        <a href="Images/thumb_02.jpg" target="_blank" ></a>
        <img src="Images/thumb_02.jpg" />
    </c:if>
    <c:if test="#{empty user or user.userId eq 0}">
        <a href="/DisplayBlobExample?userId=#{user.userId}" target="_blank"></a>
        <img src="/DisplayBlobExample?userId=#{user.userId}" />
    </c:if>
</html>

Another solution is to specify all the conditions you want inside an EL of one element. Though it could be heavier and less readable, here it is:

<a href="#{not empty user or user.userId eq 0 ? '/Images/thumb_02.jpg' : '/DisplayBlobExample?userId='}#{not empty user or user.userId eq 0 ? '' : user.userId}" target="_blank"></a>
<img src="#{not empty user or user.userId eq 0 ? '/Images/thumb_02.jpg' : '/DisplayBlobExample?userId='}#{not empty user or user.userId eq 0 ? '' : user.userId}" target="_blank"></img>