Multiple positive solutions for nonlinear dynamical systems on a measure chain

In this paper, we consider the following dynamical system on a measure chain: u 1 ΔΔ(t)+f 1(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], u 2 ΔΔ(t)+f 2(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], with the Sturm–Liouville boundary value conditions αu i(a)−βu i Δ(a)=0, γu i(σ(b))+δu i Δ(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.