A non-resonant multi-point boundary-value problem for a p-Laplacian type operator

Let $phi $ be an odd increasing homeomorphism from $mathbb{R}$ onto $mathbb{R}$ with $phi (0)=0$, $f:[0$,$1]imes mathbb{R}^{2}o mathbb{R}$ be a function satisfying Caratheodory's conditions and $e(t)in L^{1}[0,1]$. Let $xi_{i}in (0,1)$, $a_{i}in mathbb{R}$, $i=1,2, dots , m-2$, $sum_{i=1}^{m-2}a_{i}eq 1$, $0 Keywords Multi-point boundary-value problem --- three-point boundary-value problem --- $p$-Laplacian --- Leray Schauder Continuation theorem --- Caratheodory's conditions.