Jean Leray and nonlinear integral equations: A partially forgotten legacy

Some applications given in Jean Leray’s thesis of 1933 seem to have been forgotten, before being rediscovered and then widely developed. The reason may be found in the fact that the Arzelà–Schmidt’s method introduced in the thesis was superseded one year later by the more general and fruitful Leray-Schauder’s method. We also show that, despite its fame and a steadily increasing number of applications, some aspects of Leray–Schauder’s paper were somewhat forgotten too. Dedicated, with admiration, to the living memory of Jean Leray