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1998 Discontinuous implicit elliptic boundary value problems
S. Carl, S. Heikkilä
Differential Integral Equations 11(6): 823-834 (1998). DOI: 10.57262/die/1367329478


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.


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S. Carl. S. Heikkilä. "Discontinuous implicit elliptic boundary value problems." Differential Integral Equations 11 (6) 823 - 834, 1998.


Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1064.35509
MathSciNet: MR1659268
Digital Object Identifier: 10.57262/die/1367329478

Primary: 35J65
Secondary: 47J05 , 47N20

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.11 • No. 6 • 1998
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