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: email@example.com tel 562-985-5338 fax 562-985-8227
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