Transformations of Differential Equations and Applications

Author

Despina Andrea Stavri, University of Tennessee, Knoxville

Date of Award

8-2007

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Don Hinton

Committee Members

Ohannes Karakashian, Suzanne Lenhart

Abstract

The Sturm-Liouville problems introduced by Jacques Charles Francois Sturm and Joseph Liouville in the 19^thcentury are very important in applied mathematics. Singular Sturm-Liouville problems and two physical problems are discussed. The two physical problems are solved using two methods: Exact and asymptotic solutions. Also, the Sturm-Liouville problem's are classified using the Weyl-Kodaira Theorem. A general transformation of a third order differential equation is introduced. Oscillation and non-oscillation theorems on an infinite interval for a third order differential equation are stated. New versions of these theorems are introduced for the special cases and examples are given to illustrate them. Finally, a canonical third order differential equation is discussed.

Recommended Citation

Stavri, Despina Andrea, "Transformations of Differential Equations and Applications. " Master's Thesis, University of Tennessee, 2007.
https://trace.tennessee.edu/utk_gradthes/4325