Your decision is almost correct. The regular expression should say "[az]+" - turn on the quantifier, which means that you do not agree with one character, but with one or more lowercase characters. Note that the uber-correct solution, which matches any lower case char in Unicode, and not just the English alphabet, is as follows:
"\\p{javaLowerCase}+"
Also, note that you can achieve this with much less code:
System.out.println(input.matches("\\p{javaLowerCase}*"));
(here I alternatively use the quantifier *, which means zero or more. Choose according to the desired semantics.)
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