Kim, Eun Heui2021-05-242021-05-242005-06-15Kim, E. H. (2005). A steady state of morphogen gradients for semilinear elliptic systems. <i>Electronic Journal of Differential Equations, 2005</i>(62), pp. 1-9.1072-6691https://hdl.handle.net/10877/13645In 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.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic systemsNonquasimonotoneMorphogen gradientsArticle