Lions and others have since applied the method to a wide class of partial differential equations, the so-called "fully nonlinear second order degenerate elliptic partial differential equations."
Lions at ang iba ay may dahil inilapat ang mga paraan sa isang malawak na uri ng bahagyang kaugalian equation, ang tinatawag na "ganap na order lumubha nonlinear pangalawang patambilog bahagyang kaugalian equation."