Abstract—In this paper, we study a system of nonlinear second-order ordinary differential equations with Riemann-Stieltjes integral boundary conditions which contain some positive constants. By using the Schauder fixed point theorem and some properties of the associated Green's functions, we show that this problem has at least one positive solution for sufficiently small constants. Then, we give sufficient conditions for the nonexistence of positive solutions. Similar results for other three boundary value problems are also presented.

Index Terms—Existence, integral boundary conditions, nonexistence, positive solutions, second-order differential equations.

Johnny Henderson is with Baylor University, Department of Mathematics, Waco, Texas, 76798-7328 USA.
Rodica Luca is with Gh. Asachi Technical University, Department of Mathematics, Iasi 700506, Romania (email: rluca@math.tuiasi.ro).
Alexandru Tudorache is with Gh. Asachi Technical University, Faculty of Computer Engineering and Automatic Control, Iasi 700050, Romania.

Cite: Johnny Henderson, Rodica Luca, Alexandru Tudorache, "Positive Solutions for a System of Second-Order Differential Equations with Integral Boundary Conditions," International Journal of Applied Physics and Mathematics vol. 6, no. 3, pp. 138-149, 2016.