Geodesic
Asymptotic behavior of ground state solutions for sublinear and singular nonlinear Dirichlet problems
Electronic journal of differential equations, Tome 2011 (2011)
In this article, we are concerned with the asymptotic behavior of the classical solution to the semilinear boundary-value problem

$ \Delta u+a(x)u^{\sigma }=0 $

in

$ \frac{1}{c}\frac{L(|x| +1)}{(1+|x| )^{\lambda }} \leq a(x)\leq c\frac{L(|x| +1)}{(1+|x| )^{\lambda }}, $

where $L(t):=\exp \big(\int_1^t\frac{z(s)}{s}ds\big)$, with $z\in C([1,\infty ))$ such that $\lim_{t\to \infty } z(t)=0$. The comparable asymptotic rate of $a(x)$ determines the asymptotic behavior of the solution.
Classification : 31B05, 31C35, 34B27, 60J50
Keywords: asymptotic behavior, Dirichlet problem, ground sate solution, singular equations, sublinear equations 
@article{EJDE_2011__2011__a35,
     author = {Chemmam,  Rym and Dhifli,  Abdelwaheb and Maagli,  Habib},
     title = {Asymptotic behavior of ground state solutions for sublinear and singular nonlinear {Dirichlet} problems},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1225.31002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a35/}
}
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Chemmam,  Rym; Dhifli,  Abdelwaheb; Maagli,  Habib. Asymptotic behavior of ground state solutions for sublinear and singular nonlinear Dirichlet problems. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a35/