## On a conformally invariant elliptic equation on $$R^ n$$.(English)Zbl 0608.35017

It is proved here that there exists a sequence $$u_ k$$ of solutions of $\Delta u+| u|^{4/(m-2)}u=0\quad in\quad R^ m,\quad m\geq 3,$ with finite energy, namely, $$\int_{R^ m} | \nabla u_ k|^ 2 dx<\infty$$, for which the energy tends to $$\infty$$ as $$k\to \infty$$. The proof is accomplished by reducing the problem to an equivalent problem on the Euclidean n-sphere and then employing standard variational techniques.
Reviewer: P.Schaefer

### MSC:

 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J20 Variational methods for second-order elliptic equations

### Keywords:

finite energy; variational techniques
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### References:

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