Existence of positive solutions for a class of second-order ordinary differential systems (Q949733)

The author presents sufficient conditions for the existence of positive solutions of second order nonlinear ordinary differential systems. The results are proved by using fixed point index theory for completely continuous operators in cones. Instead of considering a single cone in the product space where the operator is defined, the author considers a cone in each component. The main advantage of this approach is that the system can involve a class of nonlinearities in which one is superlinear and the other sublinear in an specific sense established in the paper. The reader interested in this paper should know that componentwise compression and expansion fixed point theorems which allow to prove similar results have been presented by \textit{R. Precup} in [J. Fixed Point Theory Appl. 2, No.~1, 141--151 (2007; Zbl 1134.47041)].