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On the existence of positive entire solutions of a semilinear elliptic equation. (English) Zbl 0616.35029

Existence of positive entire solutions to the equation \(\Delta u- u+Q(x)u^ p=0\) in \({\mathbb{R}}^ n\) is shown, where \(p>1\) and Q(x) is a given potential, which, in general, is not radially symmetric. The approach is by establishing existence of positive solutions in any ball with radius R centered at the origin and then passing to the limit \(R\to \infty\).
Reviewer: R.Kreß

MSC:

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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