A multiplicity result for a singular generalized Sturm-Liouville boundary value problem
The author studies the existence of positive solutions of the singular second order boundary value problem \[ u''(t)+h(t) f(t, u(t), u'(t))=0, \] \[ a u(0)-bu'(0)=\sum^{m-2}_{i=1} a_i u(\xi_i),\quad c u(1)+d u'(1)=\sum^{m-2}_{i=1} b_i u(\xi_i), \] where \(h\) may be singular at \(t=0\) and/or \(t=1\). The main tool is a fixed point theorem in cones due to \textit{R. I. Avery} and \textit{A. C. Peterson} [Comput. Math. Appl. 42, No.~3--5, 313--322 (2001; Zbl 1005.47051)].
Avery and Peterson's fixed point theorem
scientific article; zbMATH DE number 5705683
scientific article