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December  2008, 22(4): 885-907. doi: 10.3934/dcds.2008.22.885

Positive solutions of an integro-differential equation in all space with singular nonlinear term

Giuseppe Maria Coclite 1, and  Mario Michele Coclite 1,

1. 

Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari, Italy, Italy

Received  January 2007 Revised  November 2007 Published  September 2008

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 $R\to \infty.$
Keywords: asymptotic behavior, Integro-differential equations in all space, singular nonlinearity, existence of positive solutions.
Mathematics Subject Classification: Primary: 45G05; 45K05; 45M05; Secondary: 45M20.
Citation: Giuseppe Maria Coclite, Mario Michele Coclite. Positive solutions of an integro-differential equation in all space with singular nonlinear term. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 885-907. doi: 10.3934/dcds.2008.22.885
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