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


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
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