| Abstract: |
| We will discuss the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $p$-Laplacian and of the fractional $p$-Laplacian:
$$
-\Delta_p u+\varepsilon(-\Delta_p)^s u=\lambda|u|^{q-2}u+|u|^{p^*-2}u \;\text{ in }\Omega,\quad
u=0 \; \text{ in }\mathbb{R}^N \setminus \Omega,
$$
where $\Omega\subset\mathbb{R}^N$ is a bounded open set, $\varepsilon\in(0,1]$, $0 |
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