| Abstract: |
| In this talk, I will discuss the existence of a solution of $ (-\Delta)^s u+f(u)=0$ in a smooth bounded domain $\Omega$ with a prescribed boundary value $\mu$ in the class of Radon measures for a large class of continuous functions $f$ satisfying a weak singularity condition expressed under an integral form. I will present the existence of a boundary trace for positive moderate solutions. In the particular case where $f(u)=u^p$ and $\mu$ is a Dirac mass, I will show the existence of several critical exponents. |
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