On positive solutions of a class of nonlinear elliptic equations
The authors deal with the semilinear equation \[ \Delta_x u+ f(x,u)+ g(|x|)x\cdot\nabla u= 0\tag{1} \] in \(G_A= \{x\in\mathbb{R}^n:|x|> A\}\), \(n\geq 3\), and are interested in so-called asymptotically vanishing solutions. Under some mild hypotheses on \(f\) and \(g\), the existence of positive, asymptotically vanishing radial solutions for (1) is proved. To this end the authors use the sub-super solution technique as well as the strong maximum principle.
scientific article; zbMATH DE number 5161914
scientific article