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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 $R\to \infty.$
Mathematics Subject Classification: Primary: 45G05; 45K05; 45M05; Secondary: 45M20.

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