caa a22 4500 386383243 CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S030821050001862X doi S030821050001862X pii (NATIONALLICENCE)cambridge-10.1017/S030821050001862X Sign-definite solutions in some linear elliptic systems [Elektronische Daten] 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. Copyright © Royal Society of Edinburgh 1989 Cosner Chris Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124, U.S.A. Schaefer Philip W. Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 347-358 0308-2105 111:3-4<347 1989 111 PRM https://doi.org/10.1017/S030821050001862X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030821050001862X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cosner Chris Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124, U.S.A NATIONALLICENCE 700 1- Schaefer Philip W. Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 347-358 0308-2105 111:3-4<347 1989 111 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge