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

Let TT be a time scale with t1,t2,t3∈Tt1,t2,t3∈T. We investigate the existence of solutions to the nonlinear even-order three-point boundary value problem View the MathML source(−1)nyΔ2n(t)=f(t,y(σ(t))),t∈[t1,t3]⊂T, Turn MathJax on View the MathML sourceyΔ2i+1(t1)=0,αyΔ2i(σ(t3))+βyΔ2i+1(σ(t3))=yΔ2i+1(t2),0≤i≤n−1, Turn MathJax on where n∈Nn∈N, t2∈(t1,σ(t3))t2∈(t1,σ(t3)), α>0α>0 and β>1β>1 are given constants.