TY  - JOUR
ID  - Dridi2015
LB  - Dridi2015
AU  - Dridi, Safa
AU  - Khamessi, Bilel
TI  - Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
ST  - Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 1
SP  - 21
EP  - 36
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.1.21
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.1.21
AB  - 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.
KW  - asymptotic behavior
KW  - Dirichlet problem
KW  - Karamata function
KW  - subsolution
KW  - supersolution
SN  - 1232-9274
ER  -