Positive solutions of nonlinear mm-point BVP for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales

In this paper, several existence theorems of positive solutions are established for nonlinear mm-point boundary value problem for the following dynamic equations on time scales (ϕ(uΔ))∇+a(t)f(t,u(t))=0,t∈[0,T],ϕ(uΔ(0))=∑i=1m−2aiϕ(uΔ(ξi)),u(T)=∑i=1m−2biu(ξi), where ϕ:R⟶Rϕ:R⟶R is an increasing homeomorphism and homomorphism and ϕ(0)=0ϕ(0)=0. The nonlinear term ff may change sign. As an application, an example to demonstrate our results is given.