Nonlocal multipoint boundary value problems. (Q2782923)

This paper is devoted to the study of the following multipoint boundary value problem for second-order ordinary differential equations NEWLINE\[NEWLINE-u''=f(t,u),\;0<t<1,\quad u(0)=\sum_{i=1}^{m} a_i u(\xi_i),\quad u(1)=\sum_{j=1}^{n} b_j u(\eta_j),NEWLINE\]NEWLINE where \(a_1,\dots, a_m\) and \(b_1,\dots, b_n\) are nonnegative reals and \(\xi_1 ,\dots, \xi_m\) and \(\eta_1 ,\dots, \eta_n\) belong to the interval \((0,1)\). The existence of at least one solution to this problem is proved under some assumptions on \(f(t,u)\) by using the upper and lower solution method.