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In a horizontal layer with free upper surface
On existence and concentration behavior of ground state solutions for a class of problems with critical growth
| 1. | Departamento de Matematica, Universidade Federal da Paraiba, 58100-907 Campina Grande-PB, Brazil |
| 2. | Departamento de Matematica e Estatistica, Universidade Federal da Paraiba,58109-970, Brazil |
$-h^2\Delta u+V(z)u=\lambda u^q+u^{2^{ *} -1,\mathbb R^N $
$u(z)>0\quad $ for all $z\in \mathbb R^N \qquad\qquad\qquad\qquad\qquad\qquad\qquad (P_{h})$
where $h, \lambda >0$, 1<$q$ <$2^{ * -1$ $=\frac{N+2}{N-2}$, $N\geq 3$ and $V: \mathbb R^N\to \mathbb R$ is a positive function such that
0< $i nf_{z\in\mathbb R^N}V(z)$< $limi nf_{|z| \rightarrow \infty}V(z)=V_{\infty}.$
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