Multiple positive solutions for an \(n\)-point nonhomogeneous boundary value problems in Banach spaces (Q606392)

The authors investigate the following \(n\)-point nonhomogeneous BVP \[ \begin{aligned} &u''(t)+a(t)f(t,u(t))=\theta, \;\;t\in (0,1), \\ &u(0)=\theta, \;\;u(1)-\sum_{i=1}^{n-2}k_iu(\xi_i)=b \end{aligned} \] in a Banach space \(E\), where \(\theta\) is the zero element of \(E\), \(b\in E\), \(f\in C[I\times E,\,E]\), \(I=[0,1]\) and \(0<\xi_1<\xi_2<\cdots<\xi_{n-2}<1,\;k_i>0\) \((i=1,2,\dots,m-2)\). By using the fixed point theorem of strict-set-contractions, they derive some sufficient conditions for the existence of at least one or two positive solutions for the problem.