Multiple positive solutions for nonlinear dynamical systems on a measure chain

In this paper, we consider the following dynamical system on a measure chain: uΔΔ1(t) + f1(t, u1 (σ(t)), u2 (σ(t))) = 0, t ∈ [a, b], uΔΔ2(t) + f2(t, u1 (σ(t)), u2 (σ(t))) = 0, t ∈ [a, b], with the Sturm-Liouville boundary value conditions αui(a) - βuΔi(a) = 0, γui(σ(b)) + δuiΔ(σ(b)) = 0 for i = 1, 2. Some results are obtained for the existence of three positive solutions of the above problem by using Leggett-Williams fixed point theorem.

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