Positive solutions for boundary value problems of a class of second-order differential equation system

This article discusses the existence of positive solutions for the system of second-order ordinary differential equation boundary value problems {GRAPHIC]where f g,:0,1are continuous. Under the related conditions that the nonlinearterms()ftxyp,,,and()gtxyq,,,may be super-linear growth or sub-linear growth onxyp,,, andq,weobtain the existence results of positive solutions. For the super-linear growth case, the Nagumo condition()F3ispresented to restrict the growth of()ftxyp,,,and()gtxyq,,,onpandq.Thesuper-linear growth or sub-lineargrowth of the nonlinear termsfandgis described by related inequality conditions instead of the usual independent inequality conditions about fandg. The discussion is based on the fixed point index theory in cones