Positive solutions of singular second order integral boundary value problem (Q2906312)

The authors investigate the class of singular integral boundary eigenvalue problems NEWLINE\[NEWLINE\begin{gathered} u''+a(t)u'(t)+b(t)u(t)+\lambda h(t)f(t,u(t))=0,\quad t\in (0,1),\\ u(0)=\int_0^1u(s)\varphi(s)\,ds,\;\;u(1)=\int_0^1u(s)\phi(s)\, ds, \end{gathered}NEWLINE\]NEWLINE where the function \(h\) may be singular at \(t=0,1\). They obtain the existence of positive solutions of the problem when the parameter \(\lambda\) lies in some interval. The main tools are fixed point index theorems on cones and spectral theory of operators.