On a class of inclusions in ordered spaces (Q1431139)

In this paper, the authors establish coincidence results for inclusions \(Lx \in Nx\) under monotonicity conditions on appropriate sequences of solutions. Coincidence results rely on a fixed point result for multivalued maps in ordered topological spaces due to \textit{S. Carl} and \textit{S. Heikkilä} [J.~Math. Anal. Appl. 234, No. 1, 31--54 (1999; Zbl 0936.47042)]. Finally, the results are applied to implicit elliptic equations: \[ Lu = f(x,u,Lu) \text{ in } \Omega, \;u=0 \text{ on }\partial\Omega, \] where \(L\) is a second order elliptic operator in divergence form and \(f\) is a positive function satisfying a monotonicity condition with respect to \(u\), and a monotonicity or continuity condition with respect to the third variable. Some growth conditions are also imposed on \(f\).