We prove the existence of a positive solution in $W^{2,q}_{loc}$ for a semilinear elliptic integro-differential problem in ${\Bbb R}^N.$ 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 $\{x\in{\Bbb R}^N;\vert x\vert \le R\},\,R>0,$ vanish as $R\to \infty.$
Positive solutions for an integro-differential equation in all space with singular nonlinear term
COCLITE, Giuseppe Maria;COCLITE, Mario
2008-01-01
Abstract
We prove the existence of a positive solution in $W^{2,q}_{loc}$ for a semilinear elliptic integro-differential problem in ${\Bbb R}^N.$ 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 $\{x\in{\Bbb R}^N;\vert x\vert \le R\},\,R>0,$ vanish as $R\to \infty.$File in questo prodotto:
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