In this paper we provide an existence result for an implicitly given elliptic differential equation of the form $f(x,u,Lu)=0$ under Dirichlet boundary conditions. The peculiarity of this implicit equation is that the function $f$ may be discontinuous in all its arguments. The main tool used to treat this problem is a fixed point result in partially ordered sets based on a generalized iteration method combined with an appropriately modified method of upper and lower solutions.
"Discontinuous implicit elliptic boundary value problems." Differential Integral Equations 11 (6) 823 - 834, 1998. https://doi.org/10.57262/die/1367329478