Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Notions of sublinearity and superlinearity for nonvariational elliptic systems

Pages: 163 - 174, Volume 13, Issue 1, June 2005      doi:10.3934/dcds.2005.13.163

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Boyan Sirakov - MODALX, Université Paris X, 92001 Nanterre Cedex, CAMS, EHESS, 75270 Paris Cedex 06, France (email)

Abstract: 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.

Keywords:  Elliptic systems, existence, topological methods, fixed point, sublinear, superlinear.
Mathematics Subject Classification:  35J45, 35J55, 37C25.

Received: March 2004;      Revised: November 2004;      Available Online: March 2005.