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A Liouville-type theorem for elliptic systems. (English) Zbl 0820.35042

The authors consider the system -u=v α , -v=u β in the whole of N , N3. The question is to determine for which values of the exponents α and β the only nonnegative solution (u,v) is the trivial one.

Theorem: If α>0,β>0 are such that α,β(N+2)/(N-2), but not both are equal to (N+2)/(N-2), then the only nonnegative C 2 solution of the system in the whole N is the trivial one. If α=β=(N+2)/(N-2), then u and v are radially symmetric with respect to some point of N .

Reviewer: O.John (Praha)

35J45Systems of elliptic equations, general (MSC2000)
35J60Nonlinear elliptic equations