Results 21 to 30 of about 886 (94)

Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
This paper deals with the following boundary value problem Dαut=ft,ut,t∈01,,u0=u1=Dα−3u0=u′1=0, where 3 < α ≤ 4, Dα is the Riemann‐Liouville fractional derivative, and the nonlinearity f, which could be singular at both t = 0 and t = 1, is required to be continuous on (0, 1) × ℝ satisfying a mild Lipschitz assumption.
Imed Bachar, Habib Mâagli, Hassan Eltayeb, Rich Avery   +3 more
wiley   +1 more source

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
openaire   +2 more sources

Homomorphisms from functional equations: the Goldie equation [PDF]

, 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   +1 more source

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

, 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.
core   +1 more source

含非线性梯度项的椭圆方程大解的渐近行为(Asymptotic behavior of large solution to elliptic problems with nonlinear gradient terms)

Zhejiang Daxue xuebao. Lixue ban, 2011
By Karamata regular variation theory and the method of lower and supper solution, the boundary behavior of boundary blow-up solutions of the nonlinear elliptic equation Δu± | ▽u|q = b(x) f(u) in Ω，subject to the singular boundary condition u | ∂Ω =+∞ is ...
ZHANGSheng-zhi(张生智), XIJin-hua(席进华)   +1 more
doaj   +1 more source

Asymptotic behavior of positive large solutions of semilinear Dirichlet problems

Electronic Journal of Qualitative Theory of Differential Equations, 2013
Let $\Omega $ be a smooth bounded domain in $\mathbb{R}^{n},\ n\geq 2$. This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems \begin{equation*} \Delta u=a(x)u^{\alpha },\alpha >1\text{ and }\Delta
Habib Maagli, Sonia Ben Othman, Rym Chemmam   +2 more
doaj   +1 more source

Non‐native species have multiple abundance–impact curves

Ecology and Evolution, Volume 10, Issue 13, Page 6833-6843, July 2020., 2020
The abundance–impact curve is a useful tool for understanding and managing the impacts of invasive species. Using models based on the impacts of the zebra mussel, I show that a single invasive species can have radically different abundance–impact curves in different habitats.
David L. Strayer
wiley   +1 more source

The exact asymptotic behaviour of the unique solution to a singular Dirichlet problem

Boundary Value Problems, 2006
By Karamata regular variation theory, we show the existence and exact asymptotic behaviour of the unique classical solution u∈C2+α(Ω)∩C(Ω¯) near the boundary to a singular Dirichlet problem −Δu=g(u)−k(x), u>0, xà ...
Jianning Yu, Zhijun Zhang
doaj   +2 more sources

Large deviations for random walks under subexponentiality: the big-jump domain [PDF]

, 2007
For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly for $x\ge x_n$
Denisov, D., Dieker, A. B., Shneer, V.
core   +7 more sources

Additivity, subadditivity and linearity: automatic continuity and quantifier weakening [PDF]

, 2017
We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are continuous and so ...
Bingham, N. H., Ostaszewski, A. J.
core   +2 more sources