We consider a three points p-Laplacian boundary value problems with integral bounday conditions on a half-line of the form\\
\[ (\phi_p(u^{\Delta}(t)))^{\Delta}+r(t)f(t,u(t),u^{\Delta}(t)) =0,\quad t \in(0,+\infty)_{\mathbb{T}},\]
\[ u(0)= \lambda \int_{0}^{\eta}u(s) \Delta s,\]
\[\lim_{t\rightarrow +\infty}u^{\Delta}(t)= u^{\Delta}(+\infty)=C,\]
where $r:(0,+\infty)_{\mathbb{T}}\rightarrow (0,+\infty)_\mathbb{T}$, $f:[0,+\infty)_{\mathbb{T}}\times\mathbb{R}\times\mathbb{R}\rightarrow \mathbb{R}$ are continuous functions, and $C\geq0$. $\phi_p(s)$ is a p-Laplacian function and $\phi_q(s)$ is the inverse function of $\phi_p(s)$. Here, $\phi_p(s)=|s|^{p-2}s$, $\phi_p^{-1}(s)=\phi_q(s)=|s|^{q-2}s$, $p>1$ and $\frac{1}{p}+\frac{1}{q}=1$. Moreover, $\phi_p(s)$ and $\phi_q(s)$ are increasing functions with respect to $s\in(-\infty,+\infty)_{\mathbb T}$
and they are odd functions. We will use the upper and lower solution method along with the Schauder`s fixed point theorem to establish the existence of at least one solution which lies between pairs of upper and lower solutions. Further, by assuming two pairs of upper and lower solutions, the Nagumo condition on the nonlinear term involved in the first-order derivative, we will establish the existence of multiple solutions on an infinite interval by using the topological degree theory. Finally, examples are included to illustrate the validation of the results.