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Query Oracle per ottenere una data particolare

In base alla descrizione nella tua domanda e nei commenti, desideri qualcosa del tipo:

case when start_date = next_day(trunc(start_date, 'MM') - 1, 'Sunday') -- date is on first sunday
     then next_day(start_date, 'Sunday') -- next Sunday, which is second in month
     else next_day(last_day(start_date), 'Sunday') -- first Sunday of next month
end

Con alcune date di esempio in un CTE, incluse alcune discusse ma anche altre:

with cte (start_date) as (
            select date '2018-05-30' from dual
  union all select date '2018-06-01' from dual
  union all select date '2018-06-02' from dual
  union all select date '2018-06-03' from dual
  union all select date '2018-06-04' from dual
  union all select date '2018-06-30' from dual
  union all select date '2018-07-01' from dual
  union all select date '2018-07-02' from dual
  union all select date '2018-07-03' from dual
  union all select date '2018-07-04' from dual
  union all select date '2018-07-05' from dual
  union all select date '2018-07-06' from dual
  union all select date '2018-07-07' from dual
  union all select date '2018-07-08' from dual
  union all select date '2018-07-31' from dual
  union all select date '2018-08-01' from dual
  union all select date '2018-08-02' from dual
  union all select date '2018-08-03' from dual
  union all select date '2018-08-04' from dual
  union all select date '2018-08-05' from dual
  union all select date '2018-08-06' from dual
)
select start_date,
  to_char(start_date, 'Dy') as day,
  case when to_char(start_date, 'Dy') = 'Sun'
       then 'Yes' else 'No' end as is_sunday,
  case when start_date = next_day(trunc(start_date, 'MM') - 1, 'Sunday')
       then 'Yes' else 'No' end as is_first_sunday,
  next_day(trunc(start_date, 'MM') - 1, 'Sunday') as first_sun_this_month,
  next_day(trunc(start_date, 'MM') + 6, 'Sunday') as second_sun_this_month,
  next_day(last_day(start_date), 'Sunday') as first_sun_next_month,
  case when start_date = next_day(trunc(start_date, 'MM') - 1, 'Sunday') -- date is on first sunday
       then next_day(start_date, 'Sunday') -- next Sunday, which is second in month
       else next_day(last_day(start_date), 'Sunday') -- first Sunday of next month
  end as result
from cte;

ottiene

START_DATE DAY          IS_ IS_ FIRST_SUN_ SECOND_SUN FIRST_SUN_ RESULT    
---------- ------------ --- --- ---------- ---------- ---------- ----------
2018-05-30 Wed          No  No  2018-05-06 2018-05-13 2018-06-03 2018-06-03
2018-06-01 Fri          No  No  2018-06-03 2018-06-10 2018-07-01 2018-07-01
2018-06-02 Sat          No  No  2018-06-03 2018-06-10 2018-07-01 2018-07-01
2018-06-03 Sun          Yes Yes 2018-06-03 2018-06-10 2018-07-01 2018-06-10
2018-06-04 Mon          No  No  2018-06-03 2018-06-10 2018-07-01 2018-07-01
2018-06-30 Sat          No  No  2018-06-03 2018-06-10 2018-07-01 2018-07-01
2018-07-01 Sun          Yes Yes 2018-07-01 2018-07-08 2018-08-05 2018-07-08
2018-07-02 Mon          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-03 Tue          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-04 Wed          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-05 Thu          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-06 Fri          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-07 Sat          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-08 Sun          Yes No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-07-31 Tue          No  No  2018-07-01 2018-07-08 2018-08-05 2018-08-05
2018-08-01 Wed          No  No  2018-08-05 2018-08-12 2018-09-02 2018-09-02
2018-08-02 Thu          No  No  2018-08-05 2018-08-12 2018-09-02 2018-09-02
2018-08-03 Fri          No  No  2018-08-05 2018-08-12 2018-09-02 2018-09-02
2018-08-04 Sat          No  No  2018-08-05 2018-08-12 2018-09-02 2018-09-02
2018-08-05 Sun          Yes Yes 2018-08-05 2018-08-12 2018-09-02 2018-08-12
2018-08-06 Mon          No  No  2018-08-05 2018-08-12 2018-09-02 2018-09-02

Il result la colonna è quella che ti interessa, le altre provano solo a mostrare un po' il funzionamento.

Sembra strano che le date dei risultati siano fuori sequenza rispetto alle date di input:2018-06-03 che va al 2018-06-10, quindi quelle precedenti e successive vanno al 2018-07-01. Ma sembra essere quello che vuoi.