# American Institute of Mathematical Sciences

April  2002, 8(2): 289-302. doi: 10.3934/dcds.2002.8.289

## Nonvariational elliptic systems

 1 Universidade Federal de Campina Grande, Departamento de Matematica e Estatistica, CEP:58109-970, Campina Grande Pb, Brazil 2 IMECC-UNICAMP, Caixa Postal 6065, CEP: 13081-970, Campinas - SP, Brazil

Revised  December 2001 Published  January 2002

In this paper, we present new concepts of sublinearity and superlinearity for elliptic systems of the form

(P)$\qquad\qquad -\Delta u = f(u, v), -\nabla v = g(u, v)$ in $\Omega$

$u = v = 0$ on $\partial \Omega$

where $\Omega$ is a smooth bounded domain and $f, g$ are continuous functions. Then we prove existence of positive solutions for such systems via topological methods.

Citation: Claudianor O. Alves, Djairo G. De Figueiredo. Nonvariational elliptic systems. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 289-302. doi: 10.3934/dcds.2002.8.289
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