Existence results for \(m\)-point boundary value problems (Q1355791)

The paper deals with existence and uniqueness of solutions of a boundary value problem of the form \[ x''(t)= f(t,x(t),x'(t))+ e(t),\quad 0<t<1,\quad x(0)=0\quad\text{and }x'(1)= \sum^{m-2}_{i=1} a_ix'(\xi_i), \] where \(0<\xi_i<\cdots<\xi_{m- 2}<1\), the coefficients \(a_i\) have the same sign, \(\sum a_i=1\). Some existence results are obtained by using the Leray-Schauder continuation theorem.