Positive solutions of a second-order singular ordinary differential equation
The authors study the existence of positive solutions for the second-order differential equation \[ u''+k\frac{u'}{t}=c(t)g(u) \] with the initial condition \(u'(0)=0\), \(u(M)=0\) in a bounded interval \([0,M]\) and \(u'(0)=u(+\infty)=0\) in \([0,+\infty)\), respectively. The methods used in this paper are based on variational methods and many ideas of \textit{H. Berestycki} and \textit{P.-L. Lions} [Arch. Ration. Mech. Anal. 82, 313--345 (1983; Zbl 0533.35029)]. The paper is very interesting.
scientific article; zbMATH DE number 2175330