Date of Award
January 2013
Degree Type
Open Access Thesis
Document Type
Master Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Jeffrey T. Neugebauer
Department Affiliation
Mathematics and Statistics
Abstract
The existence of smallest positive eigenvalues is established for the linear differential equations $u^{(4)}+\lambda_{1} q(t)u=0$ and $u^{(4)}+\lambda_{2} r(t)u=0$, $0\leq t \leq 1$, with each satisfying the boundary conditions $u(0)=u'(p)=u''(1)=u'''(1)=0$ where $1-\frac{\sqrt{3}}{3}\le p < 1$. A comparison theorem for smallest positive eigenvalues is then obtained. Using the same theorems, we will extend the problem to the fifth order via the Green's Function and again via Substitution. Applying the comparison theorems and the properties of $u_0$-positive operators to determine the existence of smallest eigenvalues. The existence of these smallest eigenvalues is then applied to characterize extremal points of the differential equation $u^{(4)} + q(t)u = 0$ satisfying boundary conditions $u(0) = u'(p) = u''(b) = u'''(b)= 0$ where $1-\frac{
Copyright
Copyright 2013 Sarah Schulz King`
Recommended Citation
King`, Sarah Schulz, "Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem" (2013). Online Theses and Dissertations. 185.
https://encompass.eku.edu/etd/185
