Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F24%3APU151068" target="_blank" >RIV/00216305:26110/24:PU151068 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.degruyter.com/document/doi/10.1515/anona-2023-0120/pdf" target="_blank" >https://www.degruyter.com/document/doi/10.1515/anona-2023-0120/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/anona-2023-0120" target="_blank" >10.1515/anona-2023-0120</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point

Popis výsledku v původním jazyce

A singular nonlinear differential equation z(sigma) dw/dz = aw + zwf(z , w), where sigma > 1, is considered in a neighbourhood of the point z = 0 z=0 located either in the complex plane C if sigma is a natural number, in a Riemann surface of a rational function if sigma is a rational number, or in the Riemann surface of logarithmic function if sigma is an irrational number. It is assumed that w = w ( z ) w=wleft(z) , a is an element of C { 0 } a, and that the function f f is analytic in a neighbourhood of the origin in C x C . Considering sigma to be an integer, a rational, or an irrational number, for each of the above-mentioned cases, the existence is proved of analytic solutions w = w (z ) w=w(z) in a domain that is part of a neighbourhood of the point z = 0 z=0 in C or in the Riemann surface of either a rational or a logarithmic function. Within this domain, the property lim z -> 0 w (z) = 0 is proved and an asymptotic behaviour of w (z) s established. Several examples and figures illustrate the results derived. The blow-up phenomenon is discussed as well.

Název v anglickém jazyce

Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point

Popis výsledku anglicky

A singular nonlinear differential equation z(sigma) dw/dz = aw + zwf(z , w), where sigma > 1, is considered in a neighbourhood of the point z = 0 z=0 located either in the complex plane C if sigma is a natural number, in a Riemann surface of a rational function if sigma is a rational number, or in the Riemann surface of logarithmic function if sigma is an irrational number. It is assumed that w = w ( z ) w=wleft(z) , a is an element of C { 0 } a, and that the function f f is analytic in a neighbourhood of the origin in C x C . Considering sigma to be an integer, a rational, or an irrational number, for each of the above-mentioned cases, the existence is proved of analytic solutions w = w (z ) w=w(z) in a domain that is part of a neighbourhood of the point z = 0 z=0 in C or in the Riemann surface of either a rational or a logarithmic function. Within this domain, the property lim z -> 0 w (z) = 0 is proved and an asymptotic behaviour of w (z) s established. Several examples and figures illustrate the results derived. The blow-up phenomenon is discussed as well.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Advances in Nonlinear Analysis

ISSN

2191-9496

e-ISSN

2191-950X

Svazek periodika

13

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

44

Strana od-do

1-44

Kód UT WoS článku

001163610100001

EID výsledku v databázi Scopus

2-s2.0-85187275375