Existence results for an even-order boundary value problem on time scales

Let T be a time scale with t1,t2,t3∈T. We investigate the existence of solutions to the nonlinear even-order three-point boundary value problem (−1)nyΔ2n(t)=f(t,y(σ(t))),t∈[t1,t3]⊂T,yΔ2i+1(t1)=0,αyΔ2i(σ(t3))+βyΔ2i+1(σ(t3))=yΔ2i+1(t2),0≤i≤n−1, where n∈N, t2∈(t1,σ(t3)), α>0 and β>1 are given constants.