Year: 2009
Type: article
Abstract: This article is a review article on the use of Prüfer Transformations techniques in proving classical theorems from the theory of Ordinary Differential Equations.We consider self-adjoint second order linear differential equations of the formWe use Prüfer transformation techniques (which are a generalization of Poincaré phase-plane analysis) to obtain some of the main theorems of the classical theory of linear differential equations.First we prove theorems from the Oscillation Theory (Sturm Comparison theorem and Disconjugacy theorems).Furthermore we study the asymptotic behavior of the equation ( ) when t → ∞ and we obtain necessary and sufficient conditions in order to have bounded solutions for ( ).Finally, we consider a certain type of regular Sturm-Liouville eigenvalue problems with boundary conditions and we study their spectrum via Prüfer transformations.
Author: George Chailos
Institution: University of Nicosia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W57677362