Applications of Prüfer transformations in the theory of ordinary differential equations

George Chailos
2009 Irish Mathematical Society Bulletin  
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 form We 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
more » ... mparison 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. 2000 Mathematics Subject Classification. 65L05, 34B24, 34L15.
doi:10.33232/bims.0063.11.31 fatcat:nb5qlffm35envosrjwi3ueotbi