A steady state of morphogen gradients for semilinear elliptic systems
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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.
CitationKim, E. H. (2005). A steady state of morphogen gradients for semilinear elliptic systems. Electronic Journal of Differential Equations, 2005(62), pp. 1-9.
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