an:01780932
Zbl 1033.35032
Busca, J??r??me; Man??sevich, Raul
A Liouville-type theorem for Lane-Emden systems
EN
Indiana Univ. Math. J. 51, No. 1, 37-51 (2002).
00087828
2002
j
35J60 35B05 35J55 35B50
nonexistence of positive solutions; critical Sobolev hyperbola; moving planes method; maximum principle
The authors provide a partial positive answer to a well-known conjecture about the nonexistence of positive solutions to Lane-Emden systems below the critical Sobolev hyperbola. The proof is based on a monotonicity argument for suitable transformed functions. It relies on a special form of the Alexandrov-Serrin moving planes method, as well as some refined forms of the maximum principle for elliptic systems that they develop here.
Their result extends the nonexistence result of \textit{D. G. de Figueiredo} and \textit{P. L. Felmer} [Ann. Sc. Norm. Sup. Pisa, Cl. Sci. (4) 21, 387--597 (1994; Zbl 0820.35042)].
Zeng Yuesheng (Huaihua)
Zbl 0820.35042