## Differential and Integral Equations

### Discontinuous implicit elliptic boundary value problems

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 11, Number 6 (1998), 823-834.

Dates
First available in Project Euclid: 30 April 2013