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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 $K(gx)= K(x)$, $x\in \bbfR\sp N$, $g\in G$, then existence theorems for $G$-symmetric solutions $u$ of the problem $$-\Delta u= K(x)\vert u\vert\sp{4/(N- 2)} u$$ are proved using variational methods.

35J60Nonlinear elliptic equations
58J70Invariance and symmetry properties
35J20Second order elliptic equations, variational methods
Full Text: DOI
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