Advances in Difference Equations
Volume 2006 (2006), Article ID 43039, 13 pages
doi:10.1155/ADE/2006/43039

Existence and nonexistence of positive solutions to a right-focal boundary value problem on time scales

Abstract

We are concerned with proving the existence of one or more than one positive solution of an n-point right-focal boundary value problem for the nonlinear dynamic equation (−1)n−1xΔn(t)=λr(t)f(t,xσ(t)). We will also obtain criteria which lead to nonexistence of positive solutions. Here the independent variable t is in a time scale. We will use fixed point theorems for operators on a Banach space.