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Uniqueness of positive solutions of $$\Delta u + u + u^ p = 0$$ in a ball. (English) Zbl 0782.35025
The author proves the uniqueness of positive solutions of the equation $$\Delta u+u+u^ p=0$$ on the ball $$B_ r\subset \mathbb{R}^ n$$ satisfying the boundary condition $$u=0$$ on $$\partial B_ r$$ for every $$p\in(1,{{n+2} \over {n-2}}\rangle$$, where $$n>2$$.

##### MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35J60 Nonlinear elliptic equations
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