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

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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

Abstract
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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 & Continuous Dynamical Systems - A, 2008, 22 (4) : 885-907. doi: 10.3934/dcds.2008.22.885

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