Zobrazeno 1 - 10
of 48
pro vyhledávání: '"JANNE HEITTOKANGAS"'
Publikováno v:
Electronic Journal of Differential Equations, Vol 2015, Iss 143,, Pp 1-24 (2015)
The classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of $f''+A(z)f'+B(z)f=0$ are of infinite order is discussed. Two distinct approaches are used. In the first approach the co
Externí odkaz:
https://doaj.org/article/07de3a7e3b11472698d000b1e3a65cd3
Publikováno v:
Abstract and Applied Analysis, Vol 2011 (2011)
In the case of the complex plane, it is known that there exists a finite set of rational numbers containing all possible growth orders of solutions of f(k)+ak-1(z)f(k-1)+⋯+a1(z)f′+a0(z)f=0 with polynomial coefficients. In the present paper, it is
Externí odkaz:
https://doaj.org/article/02488ab3cedb4674a5dfa27a7e4da816
Publikováno v:
Journal of the Australian Mathematical Society. :1-27
It is known that, in the unit disc as well as in the whole complex plane, the growth of the analytic coefficients $A_0,\dotsc ,A_{k-2}$ of $$ \begin{align*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0, \quad k\geqslant 2, \end{align*} $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ef1cd4abd7f2b775ec881da0192fe986
https://doi.org/10.1017/s1446788722000118
https://doi.org/10.1017/s1446788722000118
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 160:158-201
It is shown that the order and the lower order of growth are equal for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coefficient $A$ is analytic in the unit disc and $\log^+ M(r,A)/\log(1-r)$ tends to a finite limit as $r\to 1^-$. A
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a551b8f87b130440ec049eb6fb2aacdf
https://doi.org/10.1016/j.matpur.2022.02.001
https://doi.org/10.1016/j.matpur.2022.02.001
Publikováno v:
Expositiones Mathematicae. 40:94-126
Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) f ′ ′ + P ( z ) f = 0 , where P ( z ) is a polynomial. These results have been use
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::39b99099ee9ce916d2db7c42f9038d25
https://doi.org/10.1016/j.exmath.2021.07.002
https://doi.org/10.1016/j.exmath.2021.07.002
Publikováno v:
Acta Mathematica Sinica, English Series. 38:371-383
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c90a6660c70fd3128db51cc12343279d
https://doi.org/10.1007/s10114-022-1066-x
https://doi.org/10.1007/s10114-022-1066-x
Publikováno v:
Journal of Difference Equations and Applications. 27:1280-1309
The φ-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of me...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d7ffb73ee41e044555acc92ff9ad38ba
https://doi.org/10.1080/10236198.2021.1982919
https://doi.org/10.1080/10236198.2021.1982919
Publikováno v:
Mathematische Nachrichten. 294:748-773
Meromorphic solutions of non‐linear differential equations of the form fn+P(z,f)=h are investigated, where n≥2 is an integer, h is a meromorphic function, and P(z,f) is differential polynomial in f and its derivatives with small functions as its
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::58124b4c83652b6acffc34cc9e4e5520
https://doi.org/10.1002/mana.201900120
https://doi.org/10.1002/mana.201900120
Autor:
Zhi-Tao Wen, Janne Heittokangas
Publikováno v:
Monatshefte für Mathematik. 194:261-273
Normalized exponential sums are entire functions of the form $$\begin{aligned} f(z)=1+H_1e^{w_1z}+\cdots +H_ne^{w_nz}, \end{aligned}$$ where $$H_1,\ldots , H_n\in {{\mathbb {C}}}$$ and $$0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::50dc849a4a8540681651c364a96316ca
https://doi.org/10.1007/s00605-020-01489-2
https://doi.org/10.1007/s00605-020-01489-2
Publikováno v:
Journal of Differential Equations. 272:911-937
Supposing that A ( z ) is an exponential polynomial of the form A ( z ) = H 0 ( z ) + H 1 ( z ) e ζ 1 z n + ⋯ + H m ( z ) e ζ m z n , where H j 's are entire and of order H 0 ( z ) and the geometric location of the leading coefficients ζ 1 , …
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d100cf60a27b4bb7996d6eb2f9e362d
https://doi.org/10.1016/j.jde.2020.10.015
https://doi.org/10.1016/j.jde.2020.10.015