On uniqueness for nonlinear elliptic equation involving the Puccis extremal operatorReport as inadecuate




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In this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation M-lambda+,LambdaD2u - u + uP = 0 in R-N, limr ->infinity ur = 0, where M-lambda,Lambda+ D2u denotes the Pucci-s extremal operator with parameters 0 < lambda < Lambda and p > 1. It is known that all positive solutions of this equation are radially symmetric with respect to a point in R-N, so the problem reduces to the study of a radial version of this equation. However, this is still a nontrivial question even in the case of the Laplacian lambda = Lambda. The Pucci-s operator is a prototype of a nonlinear operator in no-divergence form. This feature makes the uniqueness question specially challenging, since two standard tools like Pohozaev identity and global integration by parts are no longer available. The corresponding equation involving M-lambda,Lambda- is also considered.



Author: Quaas, Alexander; - Tang, Moxun; - Felmer Aichele, Patricio; -

Source: http://repositorio.uchile.cl/



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