Geodesic
A steady state of morphogen gradients for semilinear elliptic systems
Electronic journal of differential equations, Tome 2005 (2005)
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 
@article{EJDE_2005__2005__a273,
     author = {Kim,  Eun Heui},
     title = {A steady state of morphogen gradients for semilinear elliptic systems},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1129.35359},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a273/}
}
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%A Kim,  Eun Heui
%T A steady state of morphogen gradients for semilinear elliptic systems
%J Electronic journal of differential equations
%D 2005
%V 2005
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%F EJDE_2005__2005__a273
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__a273/