Multiple positive solutions for \(m\)-point boundary value problems with one-dimensional \(p\)-Laplacian systems and sign changing nonlinearity (Q2792455)

The authors consider the multi-point boundary value problem for the one-dimensional \(p\)-Laplacian system NEWLINE\[NEWLINE\begin{aligned} (\phi_{p_1}(u'))'+q_1(t)f(t, u, v)=0, \quad (\phi_{p_1}(v'))'+q_2(t)f(t, u, v)=0, \quad t\in (0,1),\\ u(0)=\sum^{m-2}_{i=1}a_iu(\xi_i), \quad u'(1)=\beta u'(0), \quad v(0)=\sum^{m-2}_{i=1}a_iu(\xi_i), \quad v'(1)=\beta v'(0), \end{aligned}NEWLINE\]NEWLINE where \(\phi_{p_i}(s)=|s|^{p_i-2}s\), \(p_i>1\), \(\xi_i\in (0,1)\) with \(0<\xi_1<\cdots \xi_{m-2<1}\) and \(a_i\in [0,1)\), \(\beta\in (0,1)\). By using the fixed point index theorem in cones, they obtain results on the existence and multiplicity of positive solutions of the above \(m\)-point boundary value problem with sign changing nonlinearities.