Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales

Abstract

In this paper, we focus on the existence of positive solutions for a boundary value problem of the changing-sign differential equation on time scales. By constructing a translation transformation and combining with the properties of the solution of the nonhomogeneous boundary value problem, we transfer the changing-sign problem to a positone problem, then by means of the known fixed-point theorem, several sufficient conditions for the existence of positive solutions are established for the case in which the nonlinear term of the equation may change sign.