Positive solutions of a second-order singular ordinary differential equation (Q556356)
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scientific article; zbMATH DE number 2175330
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive solutions of a second-order singular ordinary differential equation |
scientific article; zbMATH DE number 2175330 |
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Positive solutions of a second-order singular ordinary differential equation (English)
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13 June 2005
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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.
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singular boundary value problem
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radial solution
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variational methods
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