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Sign-definite solutions in some linear elliptic systems

Published online by Cambridge University Press:  14 November 2011

Chris Cosner  and
Philip W. Schaefer
Chris Cosner
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
Philip W. Schaefer
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A.
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Synopsis

We consider a weakly coupled set of two partial differential equations where the coupling matrix has variable elements and the principal part of each equation is the same uniformly elliptic operator. Weobtain necessary conditions that the system of equations can be decoupled. By decoupling the system and using a positivity lemma due to Hess and Kato, we determine the algebraic sign of the solution components. This work extends recent results of de Figueiredo and Mitidieri. Further, one can use these results to determine the sign of the solution to certain fourth order elliptic boundary value problems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 347 - 358
Copyright
Copyright © Royal Society of Edinburgh 1989

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