| Contents |
| We consider a nonlocal Schroedinger equation in a smooth domain
with Dirichlet datum and we construct solutions that concentrate
at interior points of the domain.
The proof uses a scaling blow up of the space variable
and an appropriate Lyapunov-Schmidt bifurcation argument.
The leading of the reduced energy functional in this case is
not exponential, but polynomial with respect to
the distance from the boundary.
The exponent of such asymptotics is also
quite unexpected and
the competition among different scalings
causes of course some technical difficulties,
that can be overcome by a careful analysis
of the nonlocal Robin function.
The results presented were obtained in collaboration
with J. D\'avila, M. del Pino and E. Valdinoci. |
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