Results 1 to 10 of about 4,182 (106)

General regular variation, Popa groups and quantifier weakening [PDF]

Journal of Mathematical Analysis and Applications, 2020
We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases.
N H Bingham
exaly   +5 more sources

Karamata's characterization theorem, feller and regular variation in probability theory

Publications de l'Institut Mathematique, 2002
This article is devoted to the application of regular variation in probability theory. It starts with the proof of a version of \textit{J. Karamata}'s characterization theorem, stated without proof in [Bull. Soc. Math. Fr. 61, 55--62 (1933; Zbl 0008.00807)]. This theorem is then used to identify the spectral functions in the canonical representation of
E. Seneta
exaly   +6 more sources

Nonlinear problems with boundary blow-up: a Karamata regular variation theory approach

Asymptotic Analysis, 2006
We study the uniqueness and expansion properties of the positive solution of the logistic equation Δu+au=b(x)f(u) in a smooth bounded domain Ω, subject to the singular boundary condition u=+∞ on $\curpartial \varOmega $ . The absorption term f is a positive function satisfying the Keller–Osserman condition and such that the mapping f(u)/u is ...
Cirstea, Florica-Corina, Radulescu, Vicentiu   +1 more
exaly   +6 more sources

Beurling slow and regular variation [PDF]

, 1967
We give a new theory of Beurling regular variation ( Part II). This includes the previously known theory of Beurling slow variation ( Part I) to which we contribute by extending Bloom's theorem.
Bajšanski, Balkema, Balkema, Balkema, Banach, Beck, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bingham, Bloom, Boas, Bojanić, Bouziad, Bruckner, Bruckner, Bruckner, Ceder, Chandrasekharan, Darboux, Domsta, Elfard, Evans, Gibson, Gibson, de Haan, Halmos, Halperin, Halperin, Hardy, Hewitt, Kechris, Koosis, Korevaar, Kuczma, Kuratowski, Kuratowski, Lee, Marcus, Mehdi, van Mill, Miller, Miller, Miller, Natanson, Ostaszewski, Ostaszewski, Oxtoby, Pitt, Pólya, Poreda, Rudin, Rudin, Solecki, Tenenbaum, Weil   +62 more
core   +3 more sources

Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this paper, under some structural assumptions of weight function $b(x)$ and nonlinear term $f(u)$, we establish the asymptotic behavior and uniqueness of boundary blow-up solutions to semilinear elliptic equations \begin{equation*} \begin{cases ...
Qiaoyu Tian, Yonglin Xu
doaj   +5 more sources

Asymptotic behaviour of positive large solutions of quasilinear logistic problems [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2015
We are interested in the asymptotic analysis of singular solutions with blow-up boundary for a class of quasilinear logistic equations with indefinite potential.
Ramzi Alsaedi, Habib Maagli, Vicenţiu Rădulescu, Noureddine Zeddini   +3 more
doaj   +4 more sources

Exact boundary behavior of the unique positive solution for singular second-order differential equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this paper, we give the exact asymptotic behavior of the unique positive solution to the following singular boundary value problem \begin{equation*} \begin{cases} -\frac{1}{A}(Au^{\prime })^{\prime }=p(x)g(u),\quad x\in (0,1), \\ u>0,\quad \text{in ...
Imed Bachar, Habib Maagli
doaj   +3 more sources

Beurling regular variation, Bloom dichotomy, and the Gołąb–Schinzel functional equation [PDF]

Aequationes Mathematicae, 2014
The class of 'self-neglecting' functions at the heart of Beurling slow variation is expanded by permitting a positive asymptotic limit function λ(t), in place of the usual limit 1, necessarily satisfying the following 'self-neglect' condition:(Formula ...
Ostaszewski, A. J.
exaly   +3 more sources

Homomorphisms from functional equations: the Goldie equation [PDF]

Aequationes Mathematicae, 2016
The theory of regular variation, in its Karamata and Bojani´c-Karamata/de Haan forms, is long established and makes essential use of the Cauchy functional equation. Both forms are subsumed within the recent theory of Beurling regular variation, developed
A. Beck, A. J. Ostaszewski, A. Járai, A. Lundberg, A. Mureńko, A.J. Ostaszewski, C. Coleman, C.G. Popa, E. Jabłońska, E. Jabłońska, H.G. Dales, J. Aczél, J. Aczél, J. Brzdèk, J. Brzdęk, J. Brzdęk, J. Brzdęk, J. Brzdęk, J. Brzdęk, J. Brzdęk, J. Chudziak, J. Chudziak, J. Chudziak, J. Chudziak, J. Korevaar, L.H. Loomis, N. Jacobson, N. Jacobson, N. Jacobson, N.H. Bingham, N.H. Bingham, N.H. Bingham, N.H. Bingham, P. Javor, P. Kahlig, W. Rudin   +35 more
core   +3 more sources

Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain [PDF]

Opuscula Mathematica, 2016
Let \(\Omega\) be a bounded domain in \(\mathbb{R}^{n}\) (\(n\geq 2\)) with a smooth boundary \(\partial \Omega\). We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system ...
Majda Chaieb, Abdelwaheb Dhifli, Samia Zermani   +2 more
doaj   +2 more sources