Positive solutions for a nonlinear differential equation on a measure chain

We are concerned with proving the existence of positive solutions of general two point boundary value problems for the nonlinear equation Lx(t) := −[r(t)xΔ(t)]Δ=/tf(t, x(t)). We will use fixed point theorems concerning cones in a Banach space. Important results concerning Greenʹs functions for general two point boundary value problems for Lx(t) := −[r(t)xΔ(t)]Δ=0 will also be given.