On Coupled Systems of Lidstone-Type Boundary Value Problems

Abstract

This research concerns the existence and location of solutions for coupled system of differential equations with Lidstone-type boundary conditions. Methodology used utilizes three fundamental aspects: upper and lower solutions method, degree theory and nonlinearities with monotone conditions. In the last section an application to a coupled system composed by two fourth order equations, which models the bending of coupled suspension bridges or simply supported coupled beams, is presented.

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

“…Lidstone boundary value problems appear mathematical model of the real world problems such as the study of bending of simply-supported beams or suspended bridges [4,5,6].The existence of positive solutions of the boundary value problems (BVPs) have 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, diferential equations and dynamic equations on time scales by using various methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the references therein..…”