Publication detail

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

DIBLÍK, J. RŮŽIČKOVÁ, M.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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=w\left(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.

Keywords

analytic solution; asymptotic behaviour; blow-up phenomenon; complex plane; differential equation; singular point

Authors

DIBLÍK, J.; RŮŽIČKOVÁ, M.

Released

5. 2. 2024

Publisher

De Gruyter

Location

WARSAW

ISBN

2191-9496

Periodical

Advances in Nonlinear Analysis

Year of study

13

Number

1

State

Federal Republic of Germany

Pages from

1

Pages to

44

Pages count

44

URL

https://www.degruyter.com/document/doi/10.1515/anona-2023-0120/pdf

Full text in the Digital Library

http://hdl.handle.net/11012/245497

BibTex

@article{BUT188249,
  author="Josef {Diblík} and Miroslava {Růžičková}",
  title="Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point",
  journal="Advances in Nonlinear Analysis",
  year="2024",
  volume="13",
  number="1",
  pages="1--44",
  doi="10.1515/anona-2023-0120",
  issn="2191-9496",
  url="https://www.degruyter.com/document/doi/10.1515/anona-2023-0120/pdf"
}