  Let $u: (M, g)\to (N, h)$ be a map between Riemannian manifolds $(M, g)$ and
$(N, h)$. The $p$-bienergy of $u$ is defined by
$E_p(u)=\int_M|\tau(u)|^pd\nu_g$, where $\tau(u)$ is the tension field of $u$
and $p>1$. Critical points of $E_p(\cdot)$ are called $p$-biharmonic maps. In
this paper we will prove nonexistence result of proper $p$-biharmonic maps when
$p\geq2$. In particular when $M=\mathbb{R}^m$, we get Liouville type results
under proper integral conditions , which extend the related results of Baird,
Fardoun and Ouakkas \cite{BFO}.
