scholarly journals Singular solutions for coercive quasilinear elliptic inequalities with nonlocal terms

2020 ◽  
Vol 197 ◽  
pp. 111857 ◽  
Author(s):  
Roberta Filippucci ◽  
Marius Ghergu
Keyword(s):  
Singular Solutions ◽  
Nonlocal Terms ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

scholarly journals Quasilinear elliptic inequalities with Hardy potential and nonlocal terms

2020 ◽  
pp. 1-19
Author(s):  
Marius Ghergu ◽  
Paschalis Karageorgis ◽  
Gurpreet Singh
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Hardy Potential ◽  
Existence Of Positive Solutions ◽  
Elliptic Inequality ◽  
Image Position ◽  
Nonlocal Terms ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

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.

scholarly journals Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms

2020 ◽  
Vol 268 (10) ◽  
pp. 6033-6066 ◽  
Author(s):  
Marius Ghergu ◽  
Paschalis Karageorgis ◽  
Gurpreet Singh
Keyword(s):  
Positive Solutions ◽  
Nonlocal Terms ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities
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