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 ? (t) + a (t) x (? (t)) = f (t, x (? (t))), t [ t 1, t m ] ? , x (t 1) = k = 2 m - 1 ? k x (t k) + ? 1 x (? (t m)), where is a time scale, 0 ? t 1 < t 2 < < t m - 1 < t m, ? 1, ? 2,., ? m - 1 ? 0 are given constants. © 2012 Ismail Yaslan.