## Symmetry of ground states of semilinear elliptic equations with mixed Sobolev growth.(English)Zbl 0864.35009

The equation $$\Delta u+f(u)=0$$, $$x\in\mathbb{R}^n$$, where $$n\geq 3$$ and $$f$$ is a continuously differentiable function, is considered. The author studies the question of symmetry of non-negative and non-trivial ground states satisfying the condition $$u(x)\to 0$$ as $$|x|\to\infty$$.

### MSC:

 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

symmetry of ground states
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