Linear additive functionals of superdiffusions and related nonlinear P.D.E.
Linear additive functionals of superdiffusions and related nonlinear P.D.E.
Let $L$ be a second order elliptic differential operator in a bounded smooth domain $D$ in $\mathbb {R}^{d}$ and let $1<\alpha \le 2$. We get necessary and sufficient conditions on measures $\eta , \nu$ under which there exists a positive solution of the boundary value problem \begin{equation*}\begin {gathered} -Lv+v^{\alpha }=\eta …