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 of an integro-differential equation in all space with singular nonlinear term / Coclite, Giuseppe Maria; Coclite, Mario Michele. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 22:4(2008), pp. 885-907. [10.3934/dcds.2008.22.885]
Positive solutions of an integro-differential equation in all space with singular nonlinear term
Coclite, Giuseppe Maria;
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 $R\to \infty.$I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
