Abstract
We study the existence, uniqueness and asymptotic behavior of positive solutions to the nonlinear problem
1/A(A Phi(p)(u'))' + q(x)u(alpha) = 0, in (0, 1),
lim(x -> 0) A Phi(p)(u')(x) = 0, u(1) = 0,
where alpha < p - 1, Phi(p)(t) = t vertical bar t vertical bar p(-2), A is a positive differentiable function and q is a positive measurable function in (0, 1) such that for some c > 0,
1/c <= q(x)(1 - x)(beta) exp ( - integral(eta)(1-x) z(s)/s ds) <= c.
Our arguments combine monotonicity methods with Karamata regular variation theory.