In this paper, we study the existence of positive
solution for the following p-Laplacain type equations with critical nonlinearity
\begin{equation*}
\left\{
\renewcommand{\arraystretch}{1.25}
\begin{array}{ll}
-\Delta_p u + V （x)|u|^{p-2}u = K(x)f(u)+P(x)|u|^{p^*-2}u, \quad
x\in\mathbb{R}^N,\\
u \in \mathcal{D}^{1,p}(\mathbb{R}^N),
\end{array}
\right.
\end{equation*}
where $\Delta_p u = div(|\nabla u|^{p-2} \nabla u),\ 1 < p < N,\ p^* =\frac
{Np}{N-p}$, $V(x)$, $K(x)$ are positive continuous functions which vanish at
in...
