Even Order Half-Linear Differential Equations with Regularly Varying Coefficients

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F20%3A00555964" target="_blank" >RIV/60162694:G43__/20:00555964 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/8/8/1236" target="_blank" >https://www.mdpi.com/2227-7390/8/8/1236</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math8081236" target="_blank" >10.3390/math8081236</a>

Result language
angličtina
Original language name
Even Order Half-Linear Differential Equations with Regularly Varying Coefficients
Original language description
We establish nonoscillation criterion for the even order half-linear differential equation $(-1)^n left(f_n(t)Phileft(x^{(n)}right)right)^{(n)} + sum_{l=1}^n (-1)^{n-l} beta_{n-l}left(f_{n-l}(t)Phileft(x^{(n-l)}right)right)^{(n-l)} = 0text{,}$ where $beta_0,beta_1,hdots,beta_{n-1}$ are real numbers, $n in mathbb{N}$, $Phi(s) = leftlvert s rightrvert^{p-1} mathop{mathrm{sgn}} s$ for $s in mathbb{R}$, $p in (1,infty)$ and $f_{n-l}$ is a regularly varying (at infinity) function of the index $alpha-lp$ for $l = 0,1,hdots,n$ and $alpha in mathbb{R}$. This equation can be understood as a generalization of the even order Euler type half-linear differential equation. We obtain this Euler type equation by rewriting the equation above as follows: the terms $f_n(t)$ and $f_{n-l}(t)$ are replaced by the $t^alpha$ and $t^{alpha-lp}$, respectively. Unlike in other texts dealing with the Euler type equation, in this article an approach based on the theory of regularly varying functions is used. We establish a nonoscillation criterion by utilizing the variational technique.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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