Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem

<p>The existence of smallest positive eigenvalues is established for the linear differential equations u⁽⁴⁾+\lambda₁ q(t)u=0 and u⁽⁴⁾+\lambda₂ 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 u₀-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{ </p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor dc:publisher

Eastern Kentucky University

Year

2013

Author dc:creator

• King`, Sarah Schulz

• boundary value
• differential
• eigenvalue
• extremal points
• fifth order
• fourth order
• Mathematics

Statement dc:rights

• Copyright 2013 Sarah Schulz King`

Repository record dc:identifier

https://encompass.eku.edu/etd/185

OAI identifier oai:identifier

oai:encompass.eku.edu:etd-1183