April  2005, 13(1): 163-174. doi: 10.3934/dcds.2005.13.163

Notions of sublinearity and superlinearity for nonvariational elliptic systems

1. 

MODALX, Université Paris X, 92001 Nanterre Cedex, CAMS, EHESS, 75270 Paris Cedex 06, France

Received  March 2004 Revised  November 2004 Published  March 2005

We study existence of solutions of boundary-value problems for elliptic systems of type ($\po$) below. We introduce notions of sublinearity and superlinearity for such systems and show that sublinear systems always have a positive solution, while superlinear systems admit a positive solution provided the set of their positive solutions is bounded in the uniform norm. These facts have long been known for scalar equations.
Citation: Boyan Sirakov. Notions of sublinearity and superlinearity for nonvariational elliptic systems. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 163-174. doi: 10.3934/dcds.2005.13.163
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