Degenerate operators on the half-line

Abstract

AbstractWe study elliptic and parabolic problems governed by the singular elliptic operators $$\begin{aligned} y^{\alpha }\left( D_{yy}+\frac{c}{y}D_y\right) -V(y),\quad \alpha \in {\mathbb {R}}\end{aligned}$$ y α D yy + c y D y - V ( y ) , α ∈ R in $${\mathbb {R}}_+$$ R + , where V is a potential having nonnegative real part.