Multiple solutions for a system of \((n_i p_i)\) boundary value problems (Q1578917)

Summary: We consider the system of boundary value problems \[ \begin{cases} u^{(n_i)}_i(t)+f_i(t,u_1(t),\dots,u_m(t))=0\\ u^{(j)}_i(0)=0,\quad u^{(p_i)}_i(1)=0\end{cases} \] for \(t\in[0,1]\), \(i=1,\dots,m\) and \(0\leq j\leq n_i-2\) where \(n_i\geq 2\) and \(1\leq p_i\leq n_i-1\). Several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs.