Multi bump solutions for a class of Kirchhoff type problems with critical growth in \mathbb{R}^N$
Using variational methods, we establish existence of multi bump solutions for a class of Kirchhoff type problems \bigg(1+b\int_{\mathbb{R}^N}\nabla u|^pdx\bigg)\Delta_pu \lambda V(x) Z(x))u^{p 1} \alpha f(u) u^{p^\ast 1} where $f$ is a continuous function, $V, Z\colon \mathbb{R}^N \rightarrow\mathbb{R} are continuous functions verifying some hypotheses. We show that if the zero set of $V$ has several isolated connected components \Omega_1,\ldots,\Omega_k$ such that the interior of \Omega_i$ is not empty and \partial\Omega_i$ is smooth, then for \lambda 0$ large enough there exists, for any non empty subset \Gamma \subset {1,\ldots,k\ a bump solution trapped in a neighbourhood of \bigcup\limits_{j\in \Gamma}\Omega_j$ The results are also new for the case $p=2$