| Abstract: |
| In this talk, we will examine a family of nonlinear elliptic PDEs and closely related integral equations. The equations we consider play key roles in problems from analysis and geometry, and they also serve as basic models in mathematical physics. We will discuss several key properties of positive solutions to these problems, e.g., the optimal conditions for their existence as well as their asymptotic behavior and classification. We will also discuss the importance of these properties, especially their relationship to some open questions in nonlinear elliptic PDEs. |
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