Nonvariational elliptic systems
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.
sublinear and superlinear elliptic systems
scientific article; zbMATH DE number 1751479