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Positive solutions of an integro-differential equation in all space with singular nonlinear term
We prove the existence of a positive solution in $W_{loc}^{2,q}$ for a semilinear elliptic integro-differential problem in $\mathbb{R}^N.$
The integral operator of the equation depends on a nonlinear function that is singular in the origin. Moreover, we prove
that the averages of the solution and its gradient on the balls $\{x\in\mathbb{R}^N; |x| \le R\}, R>0,$
vanish as $R\to \infty.$