Electron. J. Diff. Eqns., Vol. 2005(2005), No. 62, pp. 1-9.

A steady state of morphogen gradients for semilinear elliptic systems

Eun Heui Kim

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.

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Eun Heui Kim
Department of Mathematics, California State University
Long Beach, CA 90840-1001, USA
email: ekim4@csulb.edu   tel 562-985-5338   fax 562-985-8227

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