Let $\phi $, $\theta $ be odd increasing homeomorphisms from $\mathbb{R}$
onto $\mathbb{R}$ satisfying $\phi (0)=\theta (0)=0$, $f:[0,1]\times \mathbb{R}\times \mathbb{R}\longrightarrow \mathbb{R}$ be a function satisfying
Carathéodory conditions and $e:[0,1]\rightarrow \mathbb{R}$ be a
function in $L^{1}[0,1]$. Let $\xi _{i}$,$\tau _{j}\in (0,1)$, $a_{i}$, $
b_{j}\in \mathbb{R}$, $i=1$, $2$, $\cdot \cdot \cdot $, $m-2$, $j$ $=$ $1$, $
2$, $\cdot $ $\cdot $ $\cdot $, $n-2$, $0<\xi _{1}<\xi _{2}<\cdot \cdot
\cdot <\xi _{m-2}<1$, $0<\tau _{1}<\tau _{2}<\cdot \cdot \cdot <\tau_{n-2}<1 $ be given. We study the problem of existence of solutions for the
generalized multi-point boundary value problem
\begin{gather}
(\phi (x^{\prime }))^{\prime }=f(t,x,x^{\prime })+e\text{, }0