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Zbl 0823.35051
Bianchi, Gabriele; Chabrowski, Jan; Szulkin, Andrzej
On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent. (English)
[J] Nonlinear Anal., Theory Methods Appl. 25, No.1, 41-59 (1995). ISSN 0362-546X

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.
[J.F.Toland (Bath)]

MSC 2000:: *35J60 Nonlinear elliptic equations
58J70 Invariance and symmetry properties
35J20 Second order elliptic equations, variational methods

Keywords: critical Sobolev exponents; concentrated compactness

Cited in: Zbl 1194.35122

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