Several Existence Theorems of Multiple Positive Solutions of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear m-point boundary value problem for the following second-order boundary value problem on time scales φ uΔ ∇ a t f t, u t 0, t ∈ 0, T , φ uΔ 0 ∑m−2 i 1 aiφ uΔ ξi , u T ∑m−2 i 1 biu ξi , where φ : R → R is an increasing homeomorphism and homomorphism and φ 0 0. Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and improve some known results by Ma and Castaneda 2001 . We must point out for readers that there is only the p-Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.