Abstract
Let p > 1, we take up ie existence, the uniqueness and the asymptotic behavior of a positive continuous solution to the following nonlinear problem in (0, +infinity), (1/A)(A phi(p)(u')) + q(x)/u(alpha) = 0, lim(x)->(0)A phi(p)(u')(x) = 0, lim(x -> +infinity)u(x) = 0, where alpha < p - 1, phi(p)(t) = t vertical bar t vertical bar(P-2) (t is an element of R), A is a positive differentiable function in (0, +infinity) and q is a positive continuous function in (0, +infinity) such that there exists c > 0 satisfying for each x in (0, vertical bar infinity), 1/c <= q(x)(1 vertical bar x)(beta) exp( integral(x+1)(1) (z(s)/s)ds) <= c, beta >= p and z subset of C([1, vertical bar infinity)) such that limt -> +infinity z(t) = 0.