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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
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