A new existence theorem for right focal boundary value problems on a measure chain Original Research Article

In this paper we consider the following differential equation on a measure chain TT uΔΔ(t)+f(u(σ(t)))=0,t∈[a,b]∩T,uΔΔ(t)+f(u(σ(t)))=0,t∈[a,b]∩T, Turn MathJax on satisfying right focal boundary value conditions u(a)=0=uΔ(σ(b)).u(a)=0=uΔ(σ(b)). Turn MathJax on An existence result is obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Our conditions imposed on f are very easy to verify and our result is even new for the special cases of differential equations and difference equations, as well as in the general time scale setting.