In java8 you no longer need to use Collections.sort method as LinkedList inherits the method sort from java.util.List, so adapting Fido's answer to Java8:
LinkedList<String>list = new LinkedList<String>();
list.add("abc");
list.add("Bcd");
list.add("aAb");
list.sort( new Comparator<String>(){
@Override
public int compare(String o1,String o2){
return Collator.getInstance().compare(o1,o2);
}
});
References:
http://docs.oracle.com/javase/8/docs/api/java/util/LinkedList.html
http://docs.oracle.com/javase/7/docs/api/java/util/List.html