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In this paper, we consider the existence of localized sign-changing solutionsfor the $p-$Laplacian nonlinear Schr\"odinger equation $$-\epsilon^p\Delta_pu+V(x)|u|^{p-2}u=|u|^{p^*-2}u+\mu|u|^{q-2}u,~~u\inW^{1,p}(\mathbb{R}^N), $$ where $1<p<N$,$p_N=\max\{p,p^*-1\}<q<p^*=\frac{Np}{N-p}$, $\mu>0$, $\Delta_p$ is the$p-$Laplacian operator. By using the penalization method together with thetruncation method and a blow-up argument, we establish for small $\epsilon$ theexistence of a sequence of localized nodal solutions concentrating near a givenlocal minimum point of the potential function.

{Localized nodal solutions for $p-$Laplacian equations with critical exponents in $\mathbb{R}^N$