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Refinement of the Benoist theorem on the size of Dini subdifferentials
Nonexistence of positive solutions of fully nonlinear elliptic equations in unbounded domains
1.  Università "La Sapienza" Roma I, Dipartimento di Matematica, Piazzale Aldo Moro 2, I00185 Roma, Italy 
limin$f_{x\in\Omega, x\to\infty}\frac{u(x)+1}{\dist(x,\partial\Omega)}=0,$
and then, in particular, for strictly sublinear supersolutions in
a domain $\Omega$ containing an open cone. In the special case that
$\Omega=\mathbb R^N$, or that $F$ is the Bellman operator, we show that the
same result holds for the whole class of nonnegative
supersolutions.
Our principal assumption on the operator $F$ involves its zero
and first order dependence when
$x\to\infty$. The same kind of assumption was introduced in a recent
paper
in collaboration with H. Berestycki and F. Hamel [4] to establish a Liouville type result for semilinear equations. The
strategy we follow to prove our main results is the same as in
[4], even if here we consider fully nonlinear
operators, possibly unbounded solutions and more general domains.
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