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This paper deals with a class of singularly perturbed nonlinear ellipticproblems $(P_\e)$ with subcritical nonlinearity.  The coefficient of the linear part is assumed to concentrate in a point ofthe domain, as $\e\to 0$, and the domain is supposed to be unbounded and withunbounded boundary.  Domains that enlarge at infinity, and whose boundary flattens or shrinks atinfinity, are considered.  It is proved that in such domains problem $(P_\e)$ has at least 2 solutions.

Semilinear elliptic problems in unbounded domains with unbounded boundary