Even Order Half-Linear Differential Equations with Regularly Varying Coefficients

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Even Order Half-Linear Differential Equations with Regularly Varying Coefficients

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Even Order Half-Linear Differential Equations with Regularly Varying Coefficients

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

8

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

11

Strana od-do

1236

Kód UT WoS článku

000568037300001

EID výsledku v databázi Scopus

2-s2.0-85089482483