Behavior of solutions of quasilinear elliptic inequalities in an unbounded domain

1996 ◽  
Vol 60 (4) ◽  
pp. 415-424
Author(s):  
A. B. Shapoval

Author(s):  
Marius Ghergu ◽  
Paschalis Karageorgis ◽  
Gurpreet Singh

We study the quasilinear elliptic inequality \[ -\Delta_m u - \frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, \] where $p>0$ , $q, \mu \in \mathbb {R}$ , $m>1$ and $I_\alpha$ is the Riesz potential of order $\alpha \in (0,N)$ . We obtain necessary and sufficient conditions for the existence of positive solutions.



2007 ◽  
Vol 87 (6) ◽  
pp. 582-600 ◽  
Author(s):  
Paolo Antonini ◽  
Dimitri Mugnai ◽  
Patrizia Pucci








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