The premise contains a geographical error: no single country claims Corsica, the Azores, and Madeira.
Portugal has never held sovereignty over Corsica. It was Genoese (1284–1768), briefly independent (1755–1769), then ceded to France (1768). Napoleon was born there in 1769.
The Azores and Madeira have been Portuguese since their 15th-century discovery/settlement.