Positive solutions of a second-order singular ordinary differential equation Original Research Article

We study the existence of positive solutions for the second-order ordinary differential equation View the MathML sourceu″+ku′t=c(t)g(u) Turn MathJax on with the initial condition u′(0)=0u′(0)=0 in bounded intervals [0,M][0,M] and in [0,+∞[[0,+∞[. Here k>1k>1, c(t)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.