| This dissertation analyzes a 2n-th order differential equation with Lidstone boundary conditions. The origin of the differential equation is a forced beam equation. First, the cantilever beam equation is derived, the general solution is obtained and an application is provided.; Next, sufficient conditions for the comparison of smallest eigenvalues are established. The theory of positive operators with respect to a cone in a Banach space and sign properties of Green's functions are used to establish the comparisons.; Then, the existence of positive solutions for nonlinear Lidstone BVP's is established. Application of a fixed point theorem due to Krasnosel'skiui, along with cone methods, is used to find eigenvalues and intervals of eigenvalues for which positive solutions exist. Finally, the existence of multiple positive solutions is established. |
