这样尝试

SELECT CASE 
       WHEN trim(TO_CHAR(SYSDATE, 'Day')) = 'Tuesday' THEN 'Its Tuesday'
       ELSE 'Its Not Tuesday'  
       END AS case_result,
       TO_CHAR(SYSDATE, 'Day') AS DAY
FROM  DUAL;

或者按照ajmalmhd04的建议，您可以尝试点赞FmDay，

SELECT CASE 
       WHEN TO_CHAR(SYSDATE, 'FmDay') = 'Tuesday' THEN 'Its Tuesday'
       ELSE 'Its Not Tuesday'  
       END AS case_result,
       TO_CHAR(SYSDATE, 'Day') AS DAY
FROM  DUAL;