To find more information on Hernando De Soto and Lucas Vasquez da Verrazano, use the Discoverers Web Homepage - Links and Information on Voyages of Discovery.
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(The following is quoted from Samuel Eliot Morison: The European Discovery of America. The Northern Voyages, A.D. 500-1600. New York: Oxford University Press (1971))
[...] The Licentiate - i.e. lawyer - Lucas Vásquez de Ayllón, justice of the supreme court of Santo Daomingo, developed an itch for exploration. In 1521 he sent a vessel commanded by Francisco Gordillo along the coast north of Florida.Gordillo, joining his forces with those of a professional slave trader, and for want of anything more profitable, loaded seventy Indians at a point on the Carolina coast which he believed to be on latitude 33o30' N. Judge Ayll{'o}n, to do him credit, liberated the slaves, but did not lose interest in the territory.
In 1523 he obtained a patent from the king to explore some 2500 miles of the coast, follow any oceanic strait he might find, and set up a colony. After sending two caravels to make a preliminary reconnaissance in 1525, Ayll{'o}n fitted out at Santo Domingo an ambitious armada. The flagship was a big nef called _La Bretona_; there were two smaller ones, _Santa Catalina_ and _Chorruca_; a _bergantin_ (a light craft like the English pinnace, suitable for exploring shoal waters), and a lighter, or barge. Altogether they carried five hundred men, women, and childen, including a number of friars and black slaves, and eighty to ninety horses. They sailed to the mouth of a river where the slave-snatching had taken place earlier, and which they called _Rio Jord{'a}n_.
(Verrazzano may have called there the previous year; it appears on his brother's maps.)
Ill luck pursued the Ayll{'o}n expedition from the start. Upon entering this river (which nobody has certainly identified), the flagship ran aground and became a total loss. The others sailed upstream a certain distance, but finding no place suitable for settlement stood out to sea again and sailed to another river forty to fifty leagues away.
Henry Harrisse, who knew the North Carolina coast, decided that this second river was the Cape Fear, and that Ayll{'o}n's colony, which he named _San Miguel de Guadalupe_, lay somewhere on its banks below Wilmington. The surrounding country Ayll{'o}n named _Chicora_, and that name appears on maps of the Carolina region for about a century.
Everything went wrong at San Miguel. The settlers were undisciplined, the terrain malarial, the Indians (suspicious owing to the previous kidnapping) refused to provide food; cold weather set in early, and Ayll{'o}n died of a fever on 18 October 1526. His colony broke up, one ship foundered on the return passage, and only 150 survivors reached Santo Domingo.
Thus Ayll{'o}n, like Gomez and Verrazzano, merely accomplished a negative. All three helped turn the attention of mighty Spain away from North America, leaving it to France and England to exploit and colonize.