Differential and Integral Equations

Discontinuous implicit elliptic boundary value problems

S. Carl and S. Heikkilä

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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

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

First available in Project Euclid: 30 April 2013

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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

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