Geodesic
A steady state of morphogen gradients for semilinear elliptic systems
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we establish the existence of positive solutions to a system of steady-state Neumann boundary problems. This system has been observed in some biological experiments, morphogen gradients; effects of Decapentaplegic (Dpp) and short gastrulation (Sog). Mathematical difficulties arise from this system being nonquasimonotone and semilinear. We overcome such difficulties by using the fixed point iteration via upper-lower solution methods. We also discuss an example, the Dpp-Sog system, of such problems.
Classification : 35J55, 35J45
Keywords: elliptic systems, nonquasimonotone, morphogen gradients 
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     author = {Kim, Eun Heui},
     title = {A steady state of morphogen gradients for semilinear elliptic systems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a73/}
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Kim, Eun Heui. A steady state of morphogen gradients for semilinear elliptic systems. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a73/