A steady state of morphogen gradients for semilinear elliptic systems
Kim, Eun Heui
Texas State University-San Marcos, Department of Mathematics
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.
Elliptic systems, Nonquasimonotone, Morphogen gradients
Kim, 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.