Positive solutions for a second-order differential system
The authors study the existence of positive solutions of the second-order system \[ \begin{gathered} -u''+\lambda u =\varphi u+f(t,u),\;t \in (0,1),\\ -\varphi''=\mu u,\;t \in (0,1),\\ u(0) =u(1) =0,\\ \varphi(0) =\varphi(1) =0,\\ \end{gathered} \] where \(\lambda > -\pi^2\), \(\mu\) is a positive parameter, and the nonlinearity \(f\) is allowed to be singular. The main tool used in this paper is Krasnosel'skiĭ's theorem on cone compression and cone expansion.
scientific article; zbMATH DE number 5804511