Geodesic
Asymptotic behavior of positive solutions for the radial \(p\)-Laplacian equation
Electronic journal of differential equations, Tome 2012 (2012)
We study the existence, uniqueness and asymptotic behavior of positive solutions to the nonlinear problem

$\displaylines{ \frac{1}{A}(A\Phi _p(u'))'+q(x)u^{\alpha}=0,\quad \hbox{in }(0,1),\cr \lim_{x\to 0}A\Phi _p(u')(x)=0,\quad u(1)=0, }$

where

$ \frac{1}{c}\leq q(x)(1-x)^{\beta }\exp \Big( -\int_{1-x}^{\eta }\frac{z(s)}{s}ds\Big)\leq c. $

Our arguments combine monotonicity methods with Karamata regular variation theory.
Classification : 34B15, 35J65
Keywords: p-Laplacian, asymptotic behavior, positive solutions, Schauder's fixed point theorem 
@article{EJDE_2012__2012__a5,
     author = {Ben Othman,  Sonia and Maagli,  Habib},
     title = {Asymptotic behavior of positive solutions for the radial {\(p\)-Laplacian} equation},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1286.34040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a5/}
}
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Ben Othman,  Sonia; Maagli,  Habib. Asymptotic behavior of positive solutions for the radial \(p\)-Laplacian equation. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a5/