For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\geq 4$, solutions of nonlocal boundary value problems satisfying \[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_m)-\sum_{i= ...

The theory of u₀-positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions ...

As an application of a general left-definite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the left-definite theory associated with the classical Legendre self-adjoint second-order differential ...

Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and set-valued inverse limits of arbitrary ...

We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier ...

In this work, a special class of time-varying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, ...

In this dissertation, we prove the existence of positive solutions to two classes of three point right focal singular boundary value problems of at least fourth order.

This dissertation explores effective and efficient computational methodologies for solving two-dimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically ...

Exceptional orthogonal polynomials (XOPs) can be viewed as an extension of their classical orthogonal polynomial counterparts. They exclude polynomials of a certain order(s) from being eigenfunctions for their corresponding ...

In this dissertation, we are concerned with uniqueness and existence of solutions of certain types of boundary value problems for fourth order differential equations. In particular, we deal with uniqueness implies uniqueness ...