Asymptotic behavior of positive solutions for the radial p-Laplacian equation

We study the existence, uniqueness and asymptotic behavior of positive solutions to the nonlinear problem $$displaylines{ frac{1}{A}(APhi _p(u'))'+q(x)u^{alpha}=0,quad hbox{in }(0,1),cr lim_{x o 0}APhi _p(u')(x)=0,quad u(1)=0, }$$ where $alpha 0, $$ frac{1}{c}leq q(x)(1-x)^{eta }exp Big( -int_{1-x}^{eta }frac{z(s)}{s}dsBig)leq c. $$ Our arguments combine monotonicity methods with Karamata regular variation theory.