Multiple positive solutions for nonlinear three-point boundary value problems on time scales

In this paper, we consider the nonlinear second-order three-point boundary value problem uΔ∇(t)+h(t)f(t,u(t))=0,t∈[t1,t3]⊂T,uΔ(t3)=0,αu(t1)−βuΔ(t1)=uΔ(t2), where TT is a time scale, 0≤t100≤t10 and β≥0β≥0 are given constants. By using fixed-point theorems in cones, some new results are obtained for the existence of at least one,two and three positive solutions of the above problem.