@Article{Dridi2015,
author = "Dridi, Safa and Khamessi, Bilel",
title = "Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "1",
pages = "21--36",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.1.21",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.1.21",
abstract = "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 in \(\mathbb{R}^{n}\), \(n\geq 3\), \(\sigma \lt 1\) and \(q\) is a positive function in \(\mathcal{C}_{loc}^{\gamma }(\Omega )\), \(0\lt\gamma \lt 1\), satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.",
keywords = "asymptotic behavior, Dirichlet problem, Karamata function, subsolution, supersolution",
issn = "1232-9274"
}