Existence of positive solutions to vector boundary value problems II (Q2702814)

This paper is the second part of the author's work on the existence of positive solutions to second-order vector differential systems with Dirichlet boundary value conditions. A sufficient condition on definition intervals was proved in the first part of the paper [Math. Slovaca 49, No. 4, 453-479 (1999; Zbl 0952.34017)] that guarantees the existence of a positive solution to the system. This paper gives a necessary condition on the definition intervals for the existence of a positive solution to the system. There are also presented simple assumptions on the nonlinearities of the system establishing a necessary and sufficient condition for the existence of a positive solution to such system.