Henderson, Johnny.2016-06-212016-06-212016-052016-03-23May 2016http://hdl.handle.net/2104/9631Comparison of smallest eigenvalues for certain two point boundary value problems for a fifth order linear differential equation are first obtained. The results are extended to (2n+1)-order and (3n+2)-order boundary value problems. Methods used for these results involve the theory of $u_0$-positive operators with respect to a cone in conjunction with sign properties of Green's functions. Finally, initial results are established for the existence of positive solutions for singular two point boundary value problems for a fifth order nonlinear differential equation. The methods involve application of a fixed point theorem for decreasing operators.application/pdfenEigenvalue. Comparison. Boundary Value.ThesisWorldwide access.Access changed 7/12/18.2016-06-21