In this paper, we study a nonlinear fractional q-difference equation with nonlocal boundary conditions. The existence of solutions for the problem is shown by applying some well-known tools of fixed-point theory such as Banach's contraction principle, Krasnoselskii's fixed-point theorem, and the Leray-Schauder nonlinear alternative. Some illustrating examples are also discussed.

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Abstract. Positive solutions (u(t), v(t)) are sought for the nonlocal (m-point) nonlinear system of boundary value problems, u ′′ + λa(t)f (v) = 0, v ′′ + λb(t)g(u) = 0, for 0 < t < 1, and satisfying,An application of a Guo-Krasnosel'skii fixed point theorem yields sufficient values of λ for which such positive solutions exist.

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