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On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent. (English) Zbl 0823.35051

If \(G\) is a subgroup of the orthogonal group \(O(N)\) and \(K(gx)= K(x)\), \(x\in \mathbb{R}^ N\), \(g\in G\), then existence theorems for \(G\)-symmetric solutions \(u\) of the problem \[ -\Delta u= K(x)| u|^{4/(N- 2)} u \] are proved using variational methods.
Reviewer: J.F.Toland (Bath)

MSC:

35J60 Nonlinear elliptic equations
58J70 Invariance and symmetry properties for PDEs on manifolds
35J20 Variational methods for second-order elliptic equations
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