Solutions to Second-order Three-point Problems on Time Scales

In the first part of the paper, we establish the existence of multiple positive solutions to the nonlinear second-order three-point boundary value problem on time scales, u ▵▿ (t)+f(t,u(t))=0, u(0)=0, 𝛂u(𝛈)=u(T) for t∈[0,T]⊂╥, where ╥ is a time scale, 𝛂>0, η∈(0,p(T)⊂╥, and 𝛂η