## 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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### References:

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