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

Abstract

Several existence theorems of positive solutions are established for nonlinear m-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→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. As an application, an example to demonstrate our results is given.