In the 1950s Leray worked in a number of areas. He studied time dependent hyperbolic partial differential equations and also began to work on the Cauchy problem.
Sa 1950s Leray nagtrabaho sa isang bilang ng mga lugar. He-aral ng oras umaasang hayperboliko bahagyang kaugalian equation at din ay nagsimulang magtrabaho sa Cauchy problema.