Existence of Strictly Positive Solutions of Neumann Boundary Value Problems

In this thesis, we study the existence of strictly positive solutions of second-order Neumann boundary value problems with nonlinearities which are allowed to take negative values via a recently established fixed point theorem for r-nowhere normal-outward maps in Banach spaces. We derive a Green's function to be used in Hammerstein integral equations. We introduce and provide proofs on linear operators which are then used in an established fixed point theorem for r-nowhere normal-outward maps in Banach spaces. We provide commentary on the application of our results to problems in physics.