Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point
Original language description
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.
Czech name
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Czech description
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Classification
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
10100 - Mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Nonlinear Analysis
ISSN
2191-9496
e-ISSN
2191-950X
Volume of the periodical
13
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
44
Pages from-to
1-44
UT code for WoS article
001163610100001
EID of the result in the Scopus database
2-s2.0-85187275375