On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals

Abstract

This paper investigates the existence of positive solutions to time-scale boundary value problems on infinite intervals. By applying the Leggett-Williams fixed point theorem in a cone, some new results for the existence of at least three positive solutions of boundary value problems are found. With infinite intervals, the theorem can be used to prove the existence of solutions of boundary value problems for nonlinear dynamic equations dependence on the delta derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting.