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Nonvariational elliptic systems. (English) Zbl 1162.35356

The authors deal with a comprehensive treatment of large classes of sublinear and superlinear elliptic systems, that is
\[ \begin{cases} -\Delta u=f(u,v),\;-\Delta v=g(u,v) &\text{in }\Omega,\\ u=v=0 &\text{on }\partial\Omega, \end{cases} \]
where \(\Omega\subset\mathbb R^N\), \(N\geq 3\), is a smooth bounded domain. Under some natural conditions on \(f\) and \(g\) they provide existence of positive solutions of (1). To this end, they use fixed point arguments.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J50 Variational methods for elliptic systems
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J60 Nonlinear elliptic equations
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