**Some properties of oscillation solutions of Sturm-Liouville equation with transmission conditions**

Kadriye Aydemir

^{1}, Hayati Olgar

^{2}, Oktay Sh. Mukhtarov

^{3}

^{*}

^{1}Amasya University, Amasya, Turkey

^{2}Tokat Gaziosmanpaşa University, Tokat, Turkey

^{3}Azerbaijan National Academy of Sciences , Bakü, Azerbaijan

** Corresponding author: omukhtarov@yahoo.com*

Presented at the 2nd International Symposium on Innovative Approaches in Scientific Studies (ISAS2018-Winter), Samsun, Turkey, Nov 30, 2018

SETSCI Conference Proceedings, 2018, 3, Page (s): 1086-1091 , https://doi.org/

**Published Date: **31 December 2018 |
1236 10

**Abstract**

Oscillation theory for the solutions of Sturm-Liouville problems is one of the traditional trends in the qualitative theory of difierential equations. Its main goal is to

establish su–cient conditions for the existence of oscillating solutions, to investigate the

laws of distribution of the zeros, the maxima and minima of the solution, to flnd estimates of the distance between the consecutive zeros and of the number of zeros in a

given interval, as well as to obtain the relationship between the oscillatory and other

fundamental properties of the solutions of various classes of difierential equations. It is

well-known that Sturm-Liouville type difierential equations with classical boundary conditions arise after on application of the method of separation of variables to the varied

assortment of physical problems. Recently such type boundary value problems under additional transmission conditions are investigated by many researches. In this paper, we

investigate analogues of the classical Sturm comparison and oscillation theorems for discontinuous Sturm-Liouville problem together with transmission conditions. We present

a new criteria for Sturm’s comparison and oscillation theorems, discuss the main tools

used in deriving those criteria.

**Keywords - **Sturm-liouville Problem, Sturm’s comparison theorem, transmission conditions, oscillation.

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