### Abstract

Original language | English |
---|---|

Pages (from-to) | 11-31 |

Number of pages | 21 |

Journal | Irish Math. Soc. Bulletin |

Volume | 63 |

Publication status | Published - 2009 |

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### Keywords

- Ordinary Differential Equations,.
- Prufer Transformations
- Sturm Liouville Problems

### Cite this

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*Irish Math. Soc. Bulletin*, vol. 63, pp. 11-31.

**Applications of Prüfer transformations in the theory of ordinary differential Equations.** / Chailos, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Applications of Prüfer transformations in the theory of ordinary differential Equations

AU - Chailos, George

PY - 2009

Y1 - 2009

N2 - his 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 Lx = (p(t)x (t)) + g(t)x(t) = 0, t ∈ (a, b). () We use Prüfer transformation techniques (which are a gener-alization of Poincaré phase-plane analysis) to obtain some of the main theorems of the classical theory of linear differen-tial equations. First we prove theorems from the Oscillation Theory (Sturm Comparison theorem and Disconjugacy theo-rems). Furthermore we study the asymptotic behavior of the equation () when t → ∞ and we obtain necessary and suf-ficient 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.

AB - his 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 Lx = (p(t)x (t)) + g(t)x(t) = 0, t ∈ (a, b). () We use Prüfer transformation techniques (which are a gener-alization of Poincaré phase-plane analysis) to obtain some of the main theorems of the classical theory of linear differen-tial equations. First we prove theorems from the Oscillation Theory (Sturm Comparison theorem and Disconjugacy theo-rems). Furthermore we study the asymptotic behavior of the equation () when t → ∞ and we obtain necessary and suf-ficient 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.

KW - Ordinary Differential Equations,.

KW - Prufer Transformations

KW - Sturm Liouville Problems

M3 - Article

VL - 63

SP - 11

EP - 31

JO - Irish Math. Soc. Bulletin

JF - Irish Math. Soc. Bulletin

SN - 0791-5578

ER -