Existence of positive solutions for Lidstone boundary value problems on time scales

Abstract

Lidstone boundary value problems appear as a mathematical model of real world problems such as the study of bending of simply supported beams or suspended bridges [4–6]. The existence of positive solutions of the boundary value problems (BVPs) has created a great deal of interest due to wide applicability in both theory and applications [7, 8]. Some authors in the literature have obtained existence results about the solutions, positive solutions, or symmetric positive solutions of Lidstone type BVPs associated with ordinary differential equations, differential equations, and dynamic equations on time scales by using various methods (see [7–24] and the references therein).