NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

Popis výsledku v původním jazyce

In the paper, we continue research on the existence of solutions with power-type asymptotics to the following discrete Emden-Fowler type equation $$Delta^2 u(k)= k^alpha u^m(k) = 0;$$ where $k ge k_0$, k is an independent variable, $k_0$ is a fixed integer, $u: {k_0; k_0 + 1; ...} to mathbb{R}$, $Delta u(k)$, $Delta^2u(k)$ are the first and second-order differences of $u(k)$ respectively and $m$ and $alpha$ are real numbers. As a result, the present paper gives new conditions for the values $m$ and $alpha$ guaranteeing the existence of solutions with power-type asymptotics. The results are compared with those previously known and visualized in the $(m; alpha)$-plane.

Název v anglickém jazyce

NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

Popis výsledku anglicky

In the paper, we continue research on the existence of solutions with power-type asymptotics to the following discrete Emden-Fowler type equation $$Delta^2 u(k)= k^alpha u^m(k) = 0;$$ where $k ge k_0$, k is an independent variable, $k_0$ is a fixed integer, $u: {k_0; k_0 + 1; ...} to mathbb{R}$, $Delta u(k)$, $Delta^2u(k)$ are the first and second-order differences of $u(k)$ respectively and $m$ and $alpha$ are real numbers. As a result, the present paper gives new conditions for the values $m$ and $alpha$ guaranteeing the existence of solutions with power-type asymptotics. The results are compared with those previously known and visualized in the $(m; alpha)$-plane.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

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