Positive solutions of a second-order singular ordinary differential equation

We study the existence of positive solutions for the second-order ordinary differential equation u'' + k t u' = c (t)g(u) with the initial condition u'(0) = 0 in bounded intervals [0, M] and in [0, +∞ [. Here k > 1, c(t) is bounded and the growth of g at infinity is controlled by a critical exponent. In our approach a shooting argument of Beresticky, Lions and Peletier is combined with variational methods. © 2005 Elsevier Ltd. All rights reserved.