Asymptotic behavior of ground state radial solutions for problems involving the Φ-Laplacian

We are concerned with the existence of positive solutions to the following boundary value problem in ( 0 , ∞ ) , 1 A A ϕ u ′ u ′ ′ = - a ( t ) u α , t > 0 , A ϕ u ′ u ′ 0 = 0 and lim t → + ∞ u ( t ) = 0 , where α ≥ 0 , ϕ is a nonnegative continuously differentiable function on 0 , ∞ , A is a continuous function on 0 , ∞ , differentiable, positive on 0 , ∞ and a is a nonnegative function satisfying some appropriate assumptions related to Karamata regular variation theory. We give also, estimates on such solutions.