Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 62, pp. 1-9.

Title: A steady state of morphogen gradients for semilinear
       elliptic systems
       
Author: Eun Heui Kim (California State Univ., Long Beach, CA, USA)

Abstract: 
 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.

 
Submitted September 9, 2004. Published June 15, 2005.
Math Subject Classifications: 35J55, 35J45.
Key Words: Elliptic systems; nonquasimonotone; morphogen gradients.