(1.1){(ϕ (x△(t)))∇+ φ (t) f (t, x (t), x△(t))= 0, t∈(0,∞) T x (0)=∑ m− 2 i= 1 αix△(ηi), limt∈ T,
t→∞ x△(t)= 0, where T is time scale, f∈ C ([0,∞) T×[0,∞)×[0,∞),[0,∞)), αi≥ 0 (1≤ i≤ m …

In this paper, we establish the criteria for the existence of at least one and three positive
solutions for a nonlinear second order multi-point time scale boundary value problem on …