Results 1 to 10 of about 79 (76)
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 increasing
Cirstea, Florica-Corina +1 more
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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
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus [PDF]
Opuscula Mathematica, 2015 In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \[-\Delta u=q(x)u^{\sigma }\;\text{in}\;\Omega,\quad u_{|\partial\Omega}=0.\] Here \(\Omega\) is an annulus
Safa Dridi, Bilel Khamessi
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Existence and boundary behavior of positive solutions for a Sturm-Liouville problem [PDF]
Opuscula Mathematica, 2016 In this paper, we discuss existence, uniqueness and boundary behavior of a positive solution to the following nonlinear Sturm-Liouville problem \[\begin{aligned}&\frac{1}{A}(Au^{\prime })^{\prime }+a(t)u^{\sigma}=0\;\;\text{in}\;(0,1),\\ &\lim\limits_{t ...
Syrine Masmoudi, Samia Zermani
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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 +2 more
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Existence and boundary behavior of weak solutions for Schrödingerean TOPSIS equations
Boundary Value Problems, 2018 In this paper, we prove that there exists a weak solution for Schrödingerean technique for order performance by similarity (TOPSIS) equations on cylinders.
Yong Wang +6 more
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Asymptotic behaviour of positive large solutions of quasilinear logistic problems
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 +3 more
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Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations
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
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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) +1 more
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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 +2 more
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