Differential and Integral Equations
- Differential Integral Equations
- Volume 11, Number 6 (1998), 823-834.
Discontinuous implicit elliptic boundary value problems
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.
Differential Integral Equations, Volume 11, Number 6 (1998), 823-834.
First available in Project Euclid: 30 April 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47N20: Applications to differential and integral equations
Carl, S.; Heikkilä, S. Discontinuous implicit elliptic boundary value problems. Differential Integral Equations 11 (1998), no. 6, 823--834. https://projecteuclid.org/euclid.die/1367329478