Existence of Positive Solutions for Semipositone Higher-Order BVPS on Time Scales

We offer conditions on semipositone function f(t,u0,u1,…,un-2) such that the boundary value problem, uΔn(t)+f(t,u(σn-1(t)),uΔ(σn-2(t)),…,uΔn-2(σ(t)))=0, t∈(0,1)∩ , n≥2, uΔi(0)=0, i=0,1,…,n-3, αuΔn-2(0)-βuΔn-1(0)=0, γuΔn-2(σ(1))+δuΔn-1(σ(1))=0, has at least one positive solution, where is a time scale and f(t,u0,u1,…,un-2)∈C([0,1]× [0,∞)n-1, (-∞,∞)) is continuous with f(t,u0,u1,…,un-2)≥-M for some positive constant M.