Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 240, pp. 1-10.

Title: Asymptotic behavior of positive solutions for the radial 
       p-Laplacian equation
        
Authors: Sonia Ben Othman (Faculte des Sciences de Tunis, Tunisia)
         Habib Maagli (King Abdulaziz Univ., Rabigh, Saudi Arabia)

Abstract:
 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 $\alpha <p-1$, $\Phi _p(t)=t|t| ^{p-2}$, A
 is a positive differentiable function and q is a positive measurable
 function in (0,1) such that for some c&gt;0,
 $$
 \frac{1}{c}\leq q(x)(1-x)^{\beta }\exp \Big(
 -\int_{1-x}^{\eta }\frac{z(s)}{s}ds\Big)\leq c.
 $$
 Our arguments combine monotonicity methods with Karamata regular variation
 theory.

Submitted September 23, 2012. Published December 28, 2012.
Math Subject Classifications: 34B15, 35J65.
Key Words: p-Laplacian; asymptotic behavior; positive solutions;
           Schauder's fixed point theorem.