MATEC Web Conf.
Volume 292, 201923rd International Conference on Circuits, Systems, Communications and Computers (CSCC 2019)
|Number of page(s)||4|
|Section||Circuits and Systems|
|Published online||24 September 2019|
Hille-Nehari type oscillation and nonoscillation criteria for linear and half-linear differential equations
Tomas Bata University in Zlin, Faculty of Applied Informatics, Department of Mathematics, Nad Stráneˇmi 4511, 760 05 Zlín, Czech Republic
* Corresponding author:email@example.com
Differential equations attract considerable attention in many applications. In particular, it was found out that half-linear differential equations behave in many aspects very similar to that in linear case. The aim of this contribution is to investigate oscillatory properties of the second-order half-linear differential equation and to give oscillation and nonoscillation criteria for this type of equation. It is also considered the linear Sturm- Liouville equation which is the special case of the half-linear equation. Main ideas used in the proof of these criteria are given and Hille-Nehari type oscillation and nonoscillation criteria for the Sturm-Liouville equation are formulated. In the next part, Hille-Nehari type criteria for the half-linear differential equation are presented. Methods used in this investigation are based on the Riccati technique and the quadratic functional, that are very useful instruments in proving oscillation/nonoscillation both for linear and half-linear equation. Conclude that there are given further criteria which guarantee either oscillation or nonoscillation of linear and half-linear equation, respectively. These criteria can be used in the next research in improving some conditions given in theorems of this paper.
© The Authors, published by EDP Sciences, 2019
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