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| In this talk, we will examine a family of integral equations involving Riesz potentials and their closely related family of differential equations. This class of problems includes weighted variants of Hardy--Littlewood--Sobolev systems and we shall discuss the optimal criteria for the existence and non-existence of positive solutions for these systems. Namely, we discuss some Liouville type theorems established using iteration methods and Pohozaev type identities in integral form, and we discuss existence results via a topological degree framework. |
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