Positive Solutions for Nonlinear First-Order m-Point Boundary Value Problem on Time Scales

Abstract

By means of fixed-point theorems, we investigate the existence of positive solutions for nonlinear first-order $m$-point boundary value problem $x^{\mathrm{\Delta }}(t)+a(t)x(\sigma (t))=f(t,x(\sigma (t))),t\in [t_1,t_m]\subset 𝕋$, $x(t_1)={\sum }_{k=2}^{m-1}{\alpha }_{k}x(t_k)+{\alpha }_{1}x(\sigma (t_m))$, where $𝕋$ is a time scale, , ${\alpha }_1,{\alpha }_2,\dots ,{\alpha }_{m-1}\ge 0$ are given constants.