Hille-Nehari type oscillation and nonoscillation criteria for linear and half-linear differential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F19%3A63524197" target="_blank" >RIV/70883521:28140/19:63524197 - isvavai.cz</a>
Result on the web
<a href="https://www.matec-conferences.org/articles/matecconf/pdf/2019/41/matecconf_cscc2019_01061.pdf" target="_blank" >https://www.matec-conferences.org/articles/matecconf/pdf/2019/41/matecconf_cscc2019_01061.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/matecconf/201929201061" target="_blank" >10.1051/matecconf/201929201061</a>

Result language
angličtina
Original language name
Hille-Nehari type oscillation and nonoscillation criteria for linear and half-linear differential equations
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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