# American Institute of Mathematical Sciences

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