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Positive evanescent solutions of nonlinear elliptic equations. (English) Zbl 1155.35029

The authors deal with the existence of positive, so-called evanescent solutions to the elliptic equation \[ \Delta_x u+ f(x,u)+ g(|x|)x\,\nabla_x u= 0,\quad x\in\mathbb{R}^N,\quad |x|> A> 0, \] where by \(|x|\) is denoted the usual Euclidean norm, \(f\) and \(g\) are given functions. The aim of this paper is to show that such evanescent solutions exist under mild assumptions on the functions \(f\) and \(g\).

MSC:

35J60 Nonlinear elliptic equations
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